3. The math department needs to buy new textbooks and laptops for their
classrooms. The textbooks cost $116.00 each and the laptops cost
$439.00 each. If they need to purchase 30 textbooks and have $6500
to spend, what is the greatest number of laptops they can buy?
Write an inequality and solve.

Exterior Angle Inequality Theorem

\( \normalsize\blue{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \ \ \ }}\)

Direction:

Use the Exterior Angle Inequality Theorem to find the measure of each angle below.

Answer:

\( \huge \underline{\boxed{\sf \red{ \angle C = 27^{\circ} }}}\)

\( \huge \underline{\boxed{\sf \red{ \angle D = 153^{\circ} }}}\)

Solution:

Add the ∠A and ∠B and minus it to 180° to know the measure of ∠C. To find the ∠D add only the ∠A and ∠B.

Finding ∠C

\(\large\tt{{180}^{\circ} = \angle A + \angle B + \angle C}\)

\(\large\tt{{180}^{\circ} = {35}^{\circ} + {118}^{\circ} + \angle C }\)

\(\large\tt{{180}^{\circ} = {153}^{\circ} + \angle C }\)

\(\large\tt{{180}^{\circ} - {153}^{\circ} = \angle C }\)

\(\large\tt{{27}^{\circ} = \angle C }\)

\(\large{\boxed{\tt{\angle C = {27}^{\circ}}} }\)

Finding ∠D or ∠ACD

\(\large\tt{ \angle A + \angle B = \angle ACD }\)

\(\large\tt{ {35}^{\circ} + {118}^{\circ} = \angle ACD }\)

\(\large\tt{ {153}^{\circ} = \angle ACD }\)

\(\large{\boxed{\tt{\angle ACD = {153}^{\circ} }}}\)

\( \normalsize\blue{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \ \ \ }}\)

\( \\ \)

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The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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The given statement about inequality is true.

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

The statement is true ''Pick a point on one side of the solid or dashed line and enter its coordinates into the original inequality to determine which side of a linear inequality to colour in for its graph. On that side of the plane, you should shade if the coordinates satisfy the inequality''.

The statement defines how to write an inequality the meaning of inequality is that one part of the inequality will be shaded by some colour indicating that the region is falling under the area of inequality.

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Answer:

x<3

Step-by-step explanation:

Answer:

\(\boxed{x\leq 3}\)

Step-by-step explanation:

\(4x \leq 12\)

\(\sf Divide \ both \ parts \ by \ 4.\)

\(\displaystyle \frac{4x}{4} \leq \frac{12}{4}\)

\(x\leq 3\)

Answer:

(a) The probability that a randomly selected athlete uses a stairclimber for​  less than 19 ​minutes is 0.2388.

(b) The probability that a randomly selected athlete uses a stairclimber for​  between 24 and 33 ​minutes is 0.3997.

(c) The probability that a randomly selected athlete uses a stairclimber for​  more than 40 minutes is 0.0113.

Step-by-step explanation:

We are given that the amounts of time per workout an athlete uses a stairclimber are normally​ distributed, with a mean of 24 minutes and a standard deviation of 7 minutes.

Let X = amounts of time per workout an athlete uses a stairclimber

So, X ~ Normal(\(\mu=24,\sigma^{2} =7^{2}\))

The z-score probability distribution for the normal distribution is given by;

                               Z  =  \(\frac{X-\mu}{\sigma}\)  ~ N(0,1)

where, \(\mu\) = mean time = 24 minutes

            \(\sigma\) = standard deviation = 7 minutes

(a) The probability that a randomly selected athlete uses a stairclimber for​  less than 19 ​minutes is given by  P(X < 19 minutes)

        P(X < 19 min) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{19-24}{7}\) ) = P(Z < -0.71) = 1 - P(Z \(\leq\) 0.71)

                                                           = 1 - 0.7612 = 0.2388

The above probability is calculated by looking at the value of x = 0.71 in the z table which has an area of 0.7612.

(b) The probability that a randomly selected athlete uses a stairclimber for​  between 24 and 33 ​minutes is given by = P(24 min < X < 33 min)

     P(24 min < X < 33 min) = P(X < 33 min) - P(X \(\leq\) 24 min)

     P(X < 33 min) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{33-24}{7}\) ) = P(Z < 1.28) = 0.8997

     P(X \(\leq\) 24 min) = P( \(\frac{X-\mu}{\sigma}\) \(\leq\) \(\frac{24-24}{7}\) ) = P(Z \(\leq\) 0) = 0.50

The above probability is calculated by looking at the value of x = 1.28 and x = 0 in the z table which has an area of 0.8997 and 0.50 respectively.

Therefore, P(24 min < X < 33 min) = 0.8997 - 0.50 = 0.3997

(c) The probability that a randomly selected athlete uses a stairclimber for​  more than 40 minutes is given by  P(X > 40 minutes)

        P(X > 40 min) = P( \(\frac{X-\mu}{\sigma}\) > \(\frac{40-24}{7}\) ) = P(Z > 2.28) = 1 - P(Z \(\leq\) 2.28)

                                                           = 1 - 0.9887 = 0.0113

The above probability is calculated by looking at the value of x = 2.28 in the z table which has an area of 0.9887.

The event of probability that a randomly selected athlete uses a stairclimber for​  more than 40 minutes is unusual because this probability is less than 5% and any even whose probability is less than 5% is said to be unusual.

Answer:

1/8 cup of milk in each slice of Bread

Step-by-step explanation:

Answer:

A) 50

Step-by-step explanation:

X = 5

15 * 5 + 75 = 150

150 / 3 = 50

y = 50

Answer:

The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.

Step-by-step explanation:

We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is

 \(S_{n}\)​ = 165000.

Let us find the amount as arithmetic series as follows:

4000 + 5000 + 6000

The arithmetic series being, first term is \(a_{1}\) = 4000, second term is \(a_{2}\) = 5000.

We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:

\(d = a_{2} - a_{1} = 5000 - 4000 = 1000\)

The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) ( ‘ d ‘ being the difference. )

Next we can substitute a = 4000, d = 1000 and \(S_{n}\) = 165000 in “ \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) “ which can be represented as:

Determining, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\)

⇒ 165000 = \(\frac{n}{2}\) [( 2 x 4000 ) + ( n - 1 ) 1000 ]

⇒ 2 x 165000 = n(8000 + 1000n - 1000 )

⇒ 330000 = n(7000 + 1000n)

⇒ 330000 = 7000n + \(1000n^2\)

⇒ \(1000n^2\) + 7000n - 330000 = 0

⇒ \(1000n^2\) ( \(n^2\) + 7n - 330 ) = 0

⇒  \(n^2\) + 7n - 330 = 0

⇒ \(n^2\) + 22n - 15n - 330 = 0

⇒ n( n + 22 ) - 15 ( n + 22 ) = 0

⇒ ( n + 22 )( n - 15 ) = 0

⇒ n = -22, n = 15

We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.

Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.

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a m a z i n g

! ! ! ! ! ! !

The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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Answer:

Joint probability table :

_____ A _____ A'

_ Y_ 0.45 ___ 0.30

_ Y'_ 0.05___ 0.20

No

No

Step-by-step explanation:

Given :

Sample, size n = 500

A = driver is under the influence of alcohol :

Y = driver is less than 30 years old

P(A) = 275 / 500 = 0.55

P(Y) = 375 / 500 = 0.75

P(AnY) = 225 / 500 = 0.45

P(YnA') = (1 - 225/375)*0.75 = 0.4 * 0.75 = 0.30

Joint probability table :

_____ A _____ A'

_ Y_ 0.45 ___ 0.30

_ Y'_ 0.05___ 0.20

To determine if it is mutually exclusive : P(AnY) = 0

P(AnY) = 0.45 ; hence, it is not mutually exclusive

For A and Y to be independent ; P(A|Y) = P(A) ;

P(A|Y) = P(AnY) / P(Y)

P(A|Y) = 0.45 / 0.75 = 0.6

Hence, A and Y are not independent.

Answer is underlined

BD: 16.8+50.4= 67.2 mm

LM: 4-2.6= 1.4 cm

the form of the linear equation is

with the given equation we have

where m=2, m is the slope of the line

if we have parallel lines the slope needs to be the same

so in order to find a linear equation parallel to y=2x+4

we use the slope m=2 and the point given (-1,6)

where (-1,6)=(x1,y1)

then

the equation of the line parallel to y=2x-4 is y=2x+8

The value of sin A is, 7/25.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

The terminal side of angle A goes through the point (−24/25,7/25) on the unit circle.

Now, By definition we get;

⇒ cos A = - 24/25

⇒ Sin A = 7/25

Thus, The value of sin A is, 7/25.

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We can write the mathematical inequality as 3 ≤ (y - 2).

Inequality in mathematics is a relation that is used to compare two or more expressions in mathematics. For example -

(ax + b) > (cx + d)

kx < 6

Given is the inequality statement as -

"3 less than or equal to symbol y - 2"

Mathematically, we can write the inequality statement as -

3 ≤ (y - 2)

Therefore, we can write the mathematical inequality as 3 ≤ (y - 2).

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Meiling has 1 1/4 liter of orange juice.

Express mixed fraction 1 1/4 into fraction :

So,

Meiling has 1 1/4 liter of orange juice = 5/4 liter juice

She drinks 1/3 liter

Amount of juice used = 1/3 liter

Left juice = Total amount of juice - Amount of juice drank by Meiling

Left juice = 5/4 - 1/3

Amount of juice left is 11/12 liter

Answer : 11/12 liter

Answer:

-----------------------------

Given sequence:

If t(n) = 200, we can try to find the value of n:

There is no integer solution, since 32 < 40 < 64 or 2⁵ < 40 < 2⁶, the value of n should be between 5 and 6.

The sequence should include integer numbers, so there is no solution.

Given function:

Solve for x if f(x) is 200:

Answer:

1.  No

\(\textsf{2.} \quad x=\dfrac{\ln 40}{\ln 2} \approx5.32\;(\sf 2\;d.p.)\)

Step-by-step explanation:

Given sequence:

\(t(n)=5 \cdot 2^n\)

To determine if the sequence has a term with a value of 200, substitute t(n)=200 into the equation and solve for n:

\(\implies 5 \cdot 2^n=200\)

\(\implies 2^n=40\)

\(\implies \ln 2^n=\ln 40\)

\(\implies n\ln 2=\ln 40\)

\(\implies n=\dfrac{\ln 40}{\ln 2}\)

\(\implies n=5.3219280...\)

In a sequence, n is a positive integer.  Therefore, it is not possible for the sequence to have a term with the value of 200, as when t(n)=200, n is not a positive integer.

Given function:

\(f(x)=5 \cdot 2^x\)

To determine if the function has an output of 200, substitute f(x)=200 into the function and solve for x:

\(\implies 5 \cdot 2^x=200\)

\(\implies 2^x=40\)

\(\implies \ln 2^x=\ln 40\)

\(\implies x=\dfrac{\ln 40}{\ln 2}\)

\(\implies x=5.3219280...\)

Therefore, it is possible for the function to have an output of 200 when:

\(x=\dfrac{\ln 40}{\ln 2}\)

The given ellipse has been drawn with the all required data.

a regular oval form produced when a cone is cut by an oblique plane that does not intersect the base, or when a point moves in a plane so that the sum of its distances from two other points remains constant.

As per the given equation,

16x² + 9y² - 32x + 36y - 92 = 0

(4x - 4)² + (3y + 6)² - 56 = 16 + 36

(4x - 4)² + (3y + 6)² = 108

16(x - 1)² + 9(y + 2)² = 108

(x - 1)²/(108/16) + (y + 2)²/(108/9) = 1

(x - 1)²/(108/16) + (y + 2)²/(12) = 1

The above is the equation of an ellipse with a center (1,-2).

The coordinates of the vertices are (1,1.464) and (1,-5.464).

Length of major axis = 2√12

Length of minor axis = 2√(108/16)

The value of c = √(a² – b²)

c = √(12 - 108/16)

c = 2.29

The coordinate of the foci is will be as,

F₁ = (-1.29,-2)

F₂ = (3.29,-2)

The value of the eccentricity e = c/a

e = 2.29/√(108/16)

e = 0.88

Domain = (-1.6,-2)

Range = (3.6,-2)

Hence "The supplied ellipse has been drawn using all necessary information".

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Given:

• ΔIJK ≅ ΔPQR

• m∠I = 3x + 4

• m∠P = 72 - x

Let's find the value of x.

Since both triangles are congruent, their corresonding angles will be equal.

The corresonding angles are:

∠I = ∠P

∠J = ∠Q

∠K = ∠R

To find the value of x given that both triangles are congruent, we have:

Let's solve for x.

Subtract 4 and add x to both sides:

Divide both sides by 4:

Therefore, the value of x is 17

ANSWER:

17

The Value of x is 2/3.

The value of x, we need to determine the mean of the given values and set it equal to the expression for the mean.

The mean (average) is calculated by adding up all the values and dividing by the number of values. In this case, we have five values: x, x+3, x-5, 2x, and 3x.

Mean = (x + x+3 + x-5 + 2x + 3x) / 5

Next, we simplify the expression:

Mean = (5x - 2 + 3x) / 5

Mean = (8x - 2) / 5

We are given that the mean is also equal to x:

Mean = x

Setting these two expressions equal to each other, we have:

(x) = (8x - 2) / 5

To solve for x, we can cross-multiply:

5x = 8x - 2

Bringing all the x terms to one side of the equation and the constant terms to the other side:

5x - 8x = -2

-3x = -2

Dividing both sides by -3:

x = -2 / -3

Simplifying, we get:

x = 2/3

Therefore, the value of x is 2/3.

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Answer:

The percentile rank of the data value 73 is 84.

Step-by-step explanation:

In this problem, you want to find the percentile rank of the data value 73 in the data set.

The percentile rank represents the percent of numbers in the data set that have value equal or less than 73.

Take note that there are 25 data values in this data set. It's helpful to sort them in ascending order.

Of these 25 data values, 21 are less than or equal to the data value 73. To find the percentile rank of 73, apply the formula:

percentile rank = (L/N)(100)

where L is the number of data values that are less than or equal to 73, and N is the size of the data set.

Substituting in values for this problem, we have:

percentile rank = (21/25)(100)

percentile rank = (0.84)(100)

Percentile ranks are always expressed as whole numbers.

Evaluating the multiplication above and rounding to the nearest whole number we have:

percentile rank = 84

Interpreting our answer, 84% of the numbers in the data set have values less than or equal to 73.

Answer:

To make the piano player's practice seem consistent, adjust the Y-axis scale, use a line graph, and add a trend line or moving average.

Step-by-step explanation:

To adjust the graph to make it seem like the piano player is pretty consistent in practicing, we can make the following changes:

Adjust the scale of the Y-axis to make the differences in the average practice times appear smaller. For example, we can change the range of the Y-axis from 0-15 to 8-14, since all the data points fall within this range. This would compress the data vertically and make the differences in the average practice times appear smaller.

Use a line graph instead of a bar graph to better show the trend of the data over time. This would allow us to see any patterns or trends in the average practice times over the course of the year.

Add a trend line or moving average to the graph to show the overall trend in the data and smooth out any fluctuations. This would further emphasize the consistency in the piano player's practice habits.

By making these adjustments, the graph would show that the piano player is consistently practicing for around 10-11 hours per week throughout the year, with some slight variations. This would convey the message that the piano player is dedicated and consistent in their practice habits.

Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]

Answer:

i dont know

what to say

Step-by- 2560 = 1000 x (2 + 5 + 6)

Answer:

YES

Step-by-step explanation:

(3/8)·64 = 24 seats in the first class carriage are being used.

(7/13)·(78)·3 = 126 seats in the standard carriages are being used, for a total of ...

 24 + 126 = 150 . . . occupied seats

The number of available seats is ...

 64 +3·78 = 298

so half the seats on the train will be 298/2 = 149 seats.

 150 > 149, so more than half the seats on the train are being used.

Answer:

-13/2

or

-6.5

Step-by-step explanation:

yeah-ya.......... right?

Given the following question:

5.53 million in 2012

Growth rate is 3.01%

Part A and B:

Part C:

Starting from the initial amount of 553000 it would take a little under 15 years for the population to reach 8 million people. I wouldn't take this as the actual answer because it may be asking for the exact amount of time, only take it as the real answer if it's asking for a rough estimate or such.

Part D:

I am unable to answer.

Answer:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Step-by-step explanation:

To solve this problem, we'll consider the velocities of the cruise ship and the Gulf Stream as vectors and calculate their components and resultant vector. Then we'll find the magnitude (resultant velocity) and direction (resultant direction) of the resultant vector.

Given:

Cruise ship velocity (south): 22 mph

Gulf Stream velocity (east): 4 mph

A) Vector component for the cruise ship:

The cruise ship is traveling south, so its velocity vector is (0, -22).

B) Vector component for the Gulf Stream:

The Gulf Stream is flowing east, so its velocity vector is (4, 0).

C) Resultant vector:

To find the resultant vector, we'll add the two velocity vectors together:

Resultant vector = Cruise ship velocity + Gulf Stream velocity

Resultant vector = (0, -22) + (4, 0)

Resultant vector = (0 + 4, -22 + 0)

Resultant vector = (4, -22)

D) Resultant velocity:

The magnitude of the resultant vector gives us the resultant velocity. We can use the Pythagorean theorem to calculate it:

Resultant velocity = sqrt((x-component)^2 + (y-component)^2)

Resultant velocity = sqrt((4)^2 + (-22)^2)

Resultant velocity = sqrt(16 + 484)

Resultant velocity = sqrt(500)

Resultant velocity ≈ 22.4 mph (rounded to the nearest tenth)

E) Resultant direction:

The direction of the resultant vector can be found using trigonometry. We'll use the inverse tangent function (arctan) to find the angle between the resultant vector and the positive x-axis.

Resultant direction = arctan(y-component / x-component)

Resultant direction = arctan(-22 / 4)

Resultant direction ≈ -1.405 radians or -80.5 degrees (rounded to the nearest tenth)

Therefore, the answers are:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Answer:

$69

Step-by-step explanation:

23 + 23+23 = $69