What is the value of tan A?

Answer:

[tex]y=\frac{1}{2}x-8[/tex]

Step-by-step explanation:

Perpendicular lines have the same slope. So, the slope of the line we need to find is 1/2.

Thus, the equation is

[tex]y+5=\frac{1}{2}(x-6) \\ \\ y+5=\frac{1}{2}x-3 \\ \\ y=\frac{1}{2}x-8[/tex]

Yes y = 7 - 3x is a linear function

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

Definition of variables of a linear function

y = output variable

m = slope

x = input variable

c = y intercept

In comparison to the question asked

y = 7-3x

m = slope = -3

x = input variable

c = 7

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Answer:

m∠1 = 88°

m∠2 = 42°

m∠3 = 113°

Step-by-step explanation:

All of the angles in a triangle add up to 180°. This knowledge can be used to find angle 3, which I will rename c to make writing an equation easier.

[tex]180=25+42+c\\180=67+c\\113=c[/tex]

Angle 3 is 113°

Two angles on either side of the intersection of two straight lines are equal, therefore angle 2, or b:

[tex]b=42[/tex]

Angle 2 is 42°

Now that two angles are known in the leftmost triangle, we can solve for the last one: Angle 1, or a:

[tex]180=50+42+a\\180=92+a\\88=a[/tex]

Angle 1 is 88°

Answer: 12 small t-shirts and 18 large t-shirts

Step-by-step explanation:

24÷4=6

2×6=12 small t-shirts

3×6=18 large t-shirts

Answer:

To multiply terms containing exponents, the terms must have the same base and/or the same power. To multiply terms with the same base, keep the same base and add the powers together. To multiply terms with different bases but the same power, raise the product of the bases to the power.

Step-by-step explanation:

The system of equations representing these costs is y = 7.5x and y = 5..5x + 10

Given,

Anna desires to enroll in fitness courses. She contrasts two gyms to see which offers the best value. Each class at Fit Fast costs a specified amount. Stepping up costs a monthly fee as well as a price for each lesson.

We have to find the system of equations representing these costs;

Fit Fast: a certain number of feet per class = y = Ax

Stepping Up: a monthly charge plus a cost for each additional class = h = Bx + C

The second and fourth systems can be ignored since they lack the form that is implied by the statement.

Given that it reflects a choice that is always preferable to the alternative, the first system produces an obvious result. There is no need to compare because, for any positive value of x, 5.5x will be less than 7.5x + 10,

The third system is

It is necessary to solve the equations y = 7.5x and y = 5.5x + 10 to decide when one rate is more practical than the other.

That is,

The system of equations representing these costs is y = 7.5x and y = 5..5x + 10

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It would have cost Louisa $200 in interest charges.

The simple interest amount is calculated as follows;

SI = P*I*t

That is where we have

The balance is P.

The interest rate is I.

The time is t.

Regarding this issue;

Balance of $1,000, 19.99% APR, and 1 year.

She will pay the following sum;

SI = 1000 *0.199*1

SI = 199.9

SI ≅ 200

Louisa would have had to pay $200 in interest fees.

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Answer:

$0.42

Step-by-step explanation:

3ton=6000pounds

2,520/6000=$0.42

Answer:

She sent 111 texts that month

Step-by-step explanation:

The values of x in the given equation are x = -9 and x = 3. The solution set is [-9, 3]

From the question, we are to determine the value of x in the given equation.

The given equation is

|x + 3|= 6

Then, we can write that

x + 3 = 6 and -(x + 3) = 6

Solving the first equation

x + 3 = 6

Subtract 3 from both sides of the equation

x + 3 - 3 = 6 - 3

x = 3

Solving the second equation

-(x + 3) = 6

-x - 3 = 6

Add 3 to both sides of the equation

-x - 3 + 3 = 6 + 3

-x = 9

Multiply both sides of the equation by -1

-1 × -x = -1 × 9

x = -9

Hence, the solutions are x = -9 and x = 3

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Answer:

There are 13 small rooms and 9 large rooms reserved.

Step-by-step explanation:

First, we can make a system of equations. We can use s to represent the number of small rooms and l to represent the number of large rooms.

2 guests per small room added to 3 guests per large room equals 53 guests total, so 2s + 3l = 53.

The number of small rooms (s) plus the number of large rooms (l) equals the total number of rooms, so s + l = 22 or s = 22 - l.

We can substitute the first second equation into the first equation.

2 (22 - l) + 3l = 53

44 - 2l + 3l = 53

l = 9

So, the number of large rooms is 9. Then, to find the number of small rooms, we can substitute l into the second equation.

s = 22 - 9

s = 13

So, the number of small rooms is 13.

-1 39/45

that is the answer

The unit rate for this problem is how much Alyssa  earns per hour

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Alyssa works 6.4-hour shifts at the donut shop each day.

Last week she earned $480 for working 32 hours.

Now, To determine her earnings per hour we have to divide her total earnings by the total no. of hours she worked which is,

= $(480/32).

= $15 per hour.

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-2 - 10 + (-3)^3

= -12 - 27

= -39

Answer:

-39

Step-by-step explanation:

Substitute v and k

v - 10 + k³

-2 - 10 -3³

Multiply the 3 and the power of thirds together

-2 -10 + 27

Combine like terms

The 95% confidence interval for the true proportion of people who favored candidate a is 0.419, 0.481

How to calculate confidence interval?

First, calculate sample proportion by divide number people who favored candidate by number of sample. So:
[tex]\pi[/tex] = 450 / 1,000 = 0.45

Then we use the formula for confidence interval

[tex]\pi[/tex] ± [tex]z\sqrt{\frac{\pi (1-\pi )}{n}}[/tex]

In which z is z score that has a p value of [tex]1 - \frac{\alpha }{2}[/tex]

For 95% confidence interval z is the value of Z that has a p value of [tex]1 - \frac{0.05}{2}[/tex] = 0.975, so z = 1.96

After we have [tex]\pi[/tex] value and z value then put it in the formula. So:

= 0.45 ± [tex]1.96\sqrt{\frac{0.45(1-0.45)}{1000} }[/tex]

= 0.45 ± 0.0308

= 0.419, 0.481

Thus, the 95% confidence interval for the true proportion of people who favored candidate a is 0.419, 0.481

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No, Is it not possible that creating a Boxplot could show outliers but z-scores show no outlier. This is because Any z-score that is either higher than +3 or lower than -3 is viewed as an issue.

When you declare a data point to be an outlier and reject it, you are indicating that even if you have already observed the point, it is unlikely to happen again.

Z scores make it easier to determine whether a data value is larger or less than the mean and how far from the mean it is. The Z score precisely indicates the number of standard deviations a data point deviates from the mean.

So, Outliers can be highlighted using scatterplots, histograms, and boxplots. Asterisks or other symbols are displayed on the graph in boxplots to plainly show the presence of outliers in a dataset.

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Answer:

67.5

Step-by-step explanation:

Answer:67.5

Step-by-step explanation:0.675*100=67.5

Angles 1 and 5 constitutes one of the pairs

Step-by-step explanation:

Answer:

130°

Step-by-step explanation:

Triangle JKL is an isosceles triangle and leg angles are equal :

m<J = m<L

The sum of interior angles in a triangle is equal to 180.

m<J + m<L + m<K = 180

25 + 25 + m<K = 180

50 + m<K = 180 subtract 50 from both sides

m<K = 130°

The interest rate for one month is 2.42% and the interest amount is $40 approximately.

Given,

The penalty APR rate = 28.99%

Balance amount = $1800

We have to find the interest for one month;

Here,

The APR of 28.99% is the yearly interest. To find the monthly rate:

= Rate / 12 months

= 28.99% / 12

= 2.42%

The amount owed is therefore;

= 1,800 x 2.42%

= $43.56

= $40.00 approximately

That is,

The interest rate for one month is 2.42% and the interest amount is $40 approximately.

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Answer:

It is the first option

Step-by-step explanation:

Using front end estimation, the correct decimal solutions to the given problems are;

1) 25.72

2) 137.521

3) 17.1

Front end estimation is defined as one way to round numbers  in such a manner that an approximate answer can be easily found.

1) 32.47 - 6.75

First of all, deal with the whole numbers portion to get;

32 - 6 = 26

Next step is to handle the decimal part to get;

0.47 is approximately equal to 0.5 while 0.75 is approximately equal to 0.8. Thus;

0.5 - 0.8 = - 0.3

Therefore, we have;

26 + (-0.3) = 25.70

Therefore, the correct decimal solution can be written as; 25.72

2) 118.234 + 19.287

First of all, deal with the whole numbers portion to get;

118 + 19 = 137

Next step is to handle the decimal part to get;

0.234 is approximately equal to 0.2 while 0.287 is approximately equal to 0.3. Thus;

0.2 + 0.3 =0.5

Therefore, we have;

137 + 0.5 = 137.5

Therefore, the correct decimal solution can be written as; 137.521

C)  17.9 - 0.8

First of all, deal with the whole numbers portion to get;

17 - 0 = 17

Next step is to handle the decimal part to get;

0.9 - 0.8 = 0.1

Therefore, we have;

17 + 0.1 = 17.1

Therefore, the correct decimal solution can be written as; 17.1

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The time between when the rock was dropped and when it landed is 2.7 seconds.

What is function?  

    A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a function is defined as a relation f between a set A (the function's domain) and a set B (its co-domain). For any a A and b B, f = (a,b)| .Every element of set A must have exactly one image in set B for a relation to be considered a function. A relation from a non-empty set B is called a function if it has the property that no two separate ordered pairs in f have the same first element.

Here the given height h(t) = 100 feet

Now the given function is,

=> h(t)=25[tex]t^2[/tex]-81 .

Put h(t)=100 then ,

=> 100= 25[tex]t^2[/tex]-81 .

=> 100+81=25[tex]t^2[/tex]

=>[tex]t^2[/tex]= 181/25

=> t = 2.69=2.7 sec.

Hence the time between when the rock was dropped and when it landed is 2.7 seconds.

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The rate of the square increasing when the area is 16 cm² is 64 cm²/s. The result is obtained by using basic derivative rules.

The rate of a square increasing can be counted by the derivative of the area of the square as a function of time.

dA/dt = 2s ds/dt

Where s is side length.

If each side of a square is increasing at a rate of 8 cm/s, what is the rate of the square increasing when the area is 16 cm²?

We have the side of the square as the function of time.

ds/dt = 8 cm/s

When the area is 16 cm², the side length is

A = s²

16 = s²

s = √16

s = 4 cm

The rate of the square increasing is

dA/dt = 2s ds/dt

dA/dt = 2 × 4 × 8

dA/dt = 64 cm²/s

Hence, the rate of the square increasing when the area is 16 cm² is 64 cm²/s.

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Answer: A) 5.8

Step-by-step explanation: Hard guess

A continuación, se resume el centro, el radio y la longitud de cada intervalo:

Caso A: Centro: 5.5, Radio: 2.5, Longitud: 5

Caso B: Centro: - 1.5, Radio: 3.5, Longitud: 7

Caso C: Centro: 6, Radio: 6, Longitud: 12

Caso D: Centro: - 4.5, Radio: 4.5, Longitud: 9

En este problema tenemos cuatro casos de intervalos de números reales sobre una recta numérica. Los números reales representan un conjunto continuo, no discreto, lo cual significa que existe un número infinito de puntos dentro de la distribución lineal.

El centro es igual al punto medio del intervalo, el radio es la distancia entre el punto medio y cualesquiera de los extremos y la longitud es el doble del radio del intervalo.

Centro:

C = 0.5 · (m + M)

Radio

R = C - m

Longitud

L = 2 · R

Donde:

A continuación, determinamos el centro, el radio y la longitud de cada intervalo:

Caso A

C = 0.5 · (3 + 8) = 0.5 · 11 = 5.5

R = 5.5 - 3 = 2.5

L = 2 · 2.5 = 5

Caso B

C = 0.5 · [(- 5) + 2] = 0.5 · (- 3) = - 1.5

R = - 1.5 - (- 5) = - 1.5 + 5 = 3.5

L = 2 · 3.5 = 7

Caso C

C = 0.5 · (0 + 12) = 6

R = 6 - 0 = 6

L = 2 · 6 = 12

Caso D

C = 0.5 · [(- 9) + 0] = - 4.5

R = - 4.5 - (- 9) = 4.5

L = 2 · 4.5 = 9

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Answer:

x = 30

y = 15

z = 150

Step-by-step explanation:

90°, 2x°, and x and supplementary.

Using this knowledge, we can form the equation:

2x° + 90° + x° = 180°

and solve for x.

3x°+ 90° = 180°

3x° = 90°

x° = 30°

x = 30

x and z are same side interior angles. Therefore, they are supplementary.

Using this knowledge, we can form the equation:

x° + z° = 180°

30° + z° = 180°

z° = 150°

z = 150

z° and 2y° are supplementary.

Using this knowledge, we can form the equation:

z° + 2y° = 180°

150° + 2y° = 180°

2y° = 30°

y° = 15°

y = 15

Answer:

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