A store manager purchased a total of 15 pens and markers. Each pen cost $3.50, and each marker cost $1.75. If the
manager spent a total of $38.50, how many pens did the store manager purchase?

The number of children and adults that swam at the public pool is

331 and 23.

An equation is a mathematical statement of two expressions connected by an equal sign.

Example:

2x + 5 = 9 is an equation.

We have,

The total number of people = 354.

Cost for children = $1.50

Cost of adults = $2.25

Total amount = $548.25

Now,

Number of children = x

Number of adults = y

Now,

x + y = 354 _____(1)

x = 354 - y ____(2)

1.50x + 2.25y = 548.25 _____(3)

Putting (2) in (3).

1.50 (354 - y) + 2.25y = 548.25

531 - 1.50y + 2.25y = 548.25

0.75y = 548.25 - 531

0.75y = 17.25

y = 17.25/0.75

y = 23

Now,

x = 354 - y

x = 354 - 23

x = 331

Thus,

The number of children is 331.

The number of adults is 23.

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Answer:

4.125 rounded to 4.13 = the price of tax.

4.13 + 55 = 59.13

Jamall's salary when he made no sales is $3400

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

y = 3400 + 0.05x

When he made no sales, the value of x is 0

So, we have the following representation

y = 3400 + 0.05 x 0

Evaluate

y = 3400

Hence, the salary is $3400

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Answer: 175

Step-by-step explanation: So the formula for finding the area of a rhombus is A= 1/2 d1+d2. So, we multiply 14 x 25 to get 350, then we divide by 2, and get 175!  I hoped this helped you solve your problem :)

Answer:

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

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x - 4 ← is in slope- intercept form

with slope m = 2

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , then

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute (4, - 1 ) into the partial equation

- 1 = - 2 + c ⇒ c = - 1 + 2 = 1

y = - [tex]\frac{1}{2}[/tex] x + 1 ← equation of perpendicular line

"Copy an angle" construction has been performed.

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays.  Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

Observe that angles BAC and TSR are same.

This means, construction is done to copy the angle BAC.

So, "copy an angle" construction has been performed.

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a)There are [tex]2^m^n[/tex] possible relation

b)Similarly [tex]n^m[/tex]

c)[tex]\frac{n^m}{2^m^n}[/tex]

a)Set A has m elements and set B has n elements

Firstly determine the number of elements A*B by using the multiplication rule

Number of elements[tex]=A*B=m*n=mn[/tex]

For each element, [tex]A*B[/tex] we have two option

First element 2 ways

Second element 2 ways

mn element 2 ways

By using the multiplication rule

[tex]2*2*2......=2^m^n }[/tex]

Then there are [tex]2^m^n[/tex] possible relation

b)Similarly [tex]n^m[/tex]

c)[tex]\frac{n^m}{2^m^n}[/tex]

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The coordinates of the point on the directed line segment from (−3,4) to (3,8) partitions the segment into a ratio of 1 to 3 is given as follows:

(-1.5, 1).

The coordinates of the point are applied using proportions, as the fact that the point partitions the segment into a ratio of 1 to 3 means that the following equation is built:

Point - Initial Coordinate = 1/4(Final Coordinate - Initial Coordinate).

This equation is used to find both the x-coordinate and the y-coordinate of the point.

The x-coordinate of the point is obtained as follows:

x + 3 = 1/4(3 + 3)

x + 3 = 1.5

x = -1.5.

The y-coordinate of the point is obtained as follows:

y - 4 = 1/4(-8 - 4)

y - 4 = -3

y = 1.

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Answer:

Step-by-step explanation:

So if one bit of the length, is half the size of the other bit then we can make the following equation, for x being the length of rope:

x + 2x = 66

3x = 66

x = 22

That is the length, of the smaller one (half the big one), so 2x = 44. Hence d) is your answer.

Hope I helped!

It will be less than 26 °C as water has a relatively higher specific heat than sand is true statement about the final temperature of water.

Temperature is a unit used to represent hotness or coolness on any of a number of scales, including Fahrenheit and Celsius. According to temperature, heat energy will naturally move from a hotter (body with a higher temperature) to a colder (body with a lower temperature) (one at a lower temperature).

Given,

In an experiment, equal amounts of water and sand were heated under a lamp. The initial and final temperatures of each were recorded. A partial record of the temperature is shown.

Experimental Record

Substance Initial Temperature Final Temperature

Sand 20 °C 26 °C

Water 20 °C

The quantity of heat energy absorbed by one unit of a substance when its temperature rises by one unit is measured as the substance's specific heat.

This allows you to calculate the equation for a substance's specific heat:

Specific heat equals heat / (mass Δ T)

Given that both samples have the same amount (mass) and that all of the heat from the lamp is applied to them, you can assume that the specific heat of the samples will be as follows:

particular heat is equal to constant / ΔT.

Therefore, the two quantities are inversely connected.

Since sand has a lower specific heat than water, the sand on the shore of a beach is warmer during the day. When walking on a sandy beach on a bright day, your feet get scorched since it's hotter than the ocean.

When equal amounts of water and sand are heated as per the experiment's instructions, water will increase in temperature more slowly and, as a result, reach a lower end temperature than sand. This is because water has a higher specific heat than sand. This is the second option; because water has a substantially higher specific heat than water, the end temperature of water is less than 26°C.

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The flour will last for about 11 days.

What is equation ?

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

An equals sign is a part of a mathematical expression referred to as an equation. A lot of equations include algebra. In math, algebra is employed when you don't know the precise amount to calculate.

Suppose, the flour will last for x days.

She uses 15 pounds of flour each day.

So, the total amount of flour used in x days 15x pounds.

Given that, she has 157.86 pound of flour.

So, the equation will be

15 x = 157.86

x = 157.86 / 15

 = 10.524

 ≈ 11

Thus, the flour will last for about 11 days.

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The sample space for this experiment contains a total of 120 possible outcomes. This is because there are 10 possible balls to be drawn, and each of them can be chosen in 3 different ways. Thus, 10 x 10 x 10 = 1,000 possible combinations. However, since the order of the selected numbers does not matter, the number of possible outcomes is reduced to 1,000 / 6 = 120.

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A value between 0 and 1 represents the likelihood of an event, with 0 basically denoting impossibility and 1 generally indicating certainty.

Subtract the total number of events from the total number of outcomes. Divide the total number of ways the event could occur by the total number of possible outcomes once the probability event has been identified and its corresponding consequences have been determined.

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Answer:

100 km

Step-by-step explanation:

Answer: 400 points

Step-by-step explanation:

500 x 80 =  40,000

40,000/100 = 400 points

The kinematic equation of the motion of the paintbrush dropped 35 feet height from the ground and the 1.85 seconds reaction time of the 6 feet person standing directly below, indicates that they will be hit  by the paintbrush before they can move out of the way.

The kinematic equation of motion describe the motion of a body that moves under constant acceleration, without consideration of the forces causing the body to move.

The height from which the paintbrush is dropped from the roof to the ground = 35 feet

Height of the person standing directly below where the brush falls = 6 feet

The reaction time of the person = 1.85 seconds

The kinematic equation of motion of free fall of an object is presented as follows;

s = u·t + 0.5·g·t²

Where; s = The height through which the paintbrush falls

u = The initial velocity of the paintbrush = 0

g = The acceleration due to gravity ≈ 32.1741 ft/s²

The height the paintbrush falls before meeting the 6 feet tall person, s = 35 feet - 6 feet = 29 feet

Therefore, we get;

29 = 0 × t + 0.5 × 32.1741 × t²

t² = 29 ÷ (0.5 × 32.1741) ≈ 1.803

The time it takes the paintbrush to fall 29 feet, t, is therefore;

t = √(29 ÷ (0.5 × 32.1741)) ≈ 1.343

It takes the paintbrush to reach the height of the person standing directly below in just about 1.3 seconds after it is dropped, before the person can react to move away in 1.85 seconds, therefore, they will be hit by the paintbrush before they can move out of the way.

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To find the average rate of change of a function over an interval, we need to calculate the slope of the secant line connecting the points on the function at the two endpoints of the interval.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. In the case of a secant line, we can calculate the slope by using the formula:

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

For the function y = x^2 + 4x - 1, we can plug in the values of x and y at the two endpoints of the interval, (-4 and 1), to find the slope of the secant line:

m = [(1)^2 + 4(1) - 1] - [(-4)^2 + 4(-4) - 1] / (1 - (-4))

Simplifying this expression, we get:

m = (1 + 4 - 1) - (16 + 16 - 1) / (-3)

This simplifies to:

m = -20 / -3

Therefore, the average rate of change of the function y = x^2 + 4x - 1 over the interval -4 ≤ x ≤ 1 is 6.5.

By using testing of hypothesis, it can be concluded that

There is a systematic error in atleast one of the methods

First option is correct

What is testing of hypothesis?

Suppose there is a data at hand and there is a hypothesis to be tested. Testing of hypothesis determines whether the given hypothesis can be supported with the data at hand.

A t test can be used to compare results from two different methods.

Here, the difference in the results is significant, it means that

So the null hypothesis has to be rejected

There is a systematic error in atleast one of the methods

First option is correct

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Complete Question

The complete question has been attached

Answer:3

Step-by-step explanation:

The width at the instant the width is decreasing at .5 units/sec is increasing 5 units per/sec.

How to find change in length or width?

Given:

Area of triangle = 100 units²

Area of triangle = Length * Width

Length * Width = 100

dl / st = 2 unit/sec

a) Find length

when dw/dt = -0.5 unit/sec

l * w = -0.5

l dw/dt + w dl/dt = 0

100/w (-0.5) + w(2) = 0

(- 50+ 2w²) / w = 0

2w² = 50

w² = 25

w = 5

Hence, the width at the instant the width is decreasing at .5 units/sec is increasing 5 units per sec.

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The domain and the range are {0.5, 1.25, 2.0, 2.5} and {50, 100, 200, 225, 300}

The relation is not a function

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

Time (in minutes)      (x)  0.5   1.25   2.0   2.0   2.5

Distance (in meters) (y)   50   100   200  225  300

The domain is the list of the x values (without repetition)

So, we have

Domain = {0.5, 1.25, 2.0, 2.5}

The range is the list of the y values (without repetition)

So, we have

Range = {50, 100, 200, 225, 300}

For a relation to be a function, the x values must not be repeated for different y values

From the table, we have: (2.0, 200) and (2.0, 225)

The x value 2.0 is repeated for y values 200 and 225

Hence, the relation is not a function

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The slope of ½ is 0. A line with a zero slope is neither rising nor falling when seen from left to right or the other way around. Simply put, the slope of a horizontal line is zero.

y=m x + b, where m is the slope and b is the y-intercept, is the slope-intercept form.

where y= 0 and

y = m x + b

The slope is 0 when expressed in the slope-intercept form, or m = 0.

A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).

Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.

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The proof of  AB ≅ CD is given below.

What is triangle?

Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed by a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.

Given:  BD and AC bisect each other.

So, AE = AC  and BE = ED

Consider the triangles  ΔAEB and , ΔECD

Given,

AE = EC                         ...S

BE = ED                         ....S

Here, lines BC and AD intersects at point E, so

 m ∠AEB = m ∠DEC               ....A

Therefore, from SAS congruency,

ΔAEB ≅ ΔECD

Hence,  AB ≅ CD

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Answer:

To determine the garbage per capita, we need to divide the total waste generated by the population. In 2005, the total waste generated was 8.618 x 10^8 pounds and the population was 2.76 x 10^5 people, so the garbage per capita in that country in 2005 was 3.12 pounds per person. This can be calculated as follows:

8.618 x 10^8 pounds / 2.76 x 10^5 people = 3.12 pounds/person

Alternatively, we can rewrite the population in scientific notation to make the calculation easier:

8.618 x 10^8 pounds / (2.76 x 10^5) people = 8.618 x 10^8 pounds / (2.76 x 10^3 x 10^2) people

Now we can cancel out the common factors of 10^2 from the numerator and denominator to get the final result:

8.618 x 10^8 pounds / (2.76 x 10^3 x 10^2) people = 8.618 x 10^8 pounds / (2.76 x 10^3) people

= 8.618 x 10^5 pounds / (2.76) people

= 3.12 pounds/person

This shows that in 2005, the garbage per capita in that country was 3.12 pounds per person.

Answer:

A credit report is not useful for lenders and borrowers because it does not provide detailed information about a person's financial history.

The equation of a line with slope m and y-intercept is Y = mx + b. (0,b). y = 7x + 4 is the equation of the line with slope of 7 and y-intercept equals to 4?

Since the slope of the line is 7 and the y-intercept is 4, the equation of the line can be written as y = 7x + 4.

The equation of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept. In mathematics, the slope or gradient of a line is a numerical representation of the line's steepness and direction.

In the equation y = 7x + 4, 7 is the slope of the line and 4 is the y-intercept. This means that the line has a slope of 7 and the y-intercept is 4.

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Three types of infinitives in Spanish are the word that ends with the letters -er , -ar, and -ir.

Explanation:

Infinitive : In general sense infinitive represent the action or the purpose.

Infinitive in Spanish are generally non -conjugated verbs and they are ending with -er , -ar , -ir.

Basically infinitive in Spanish classified into three groups.

-er : Aprender meaning camping.

-ar : Acampar meaning Camping and so on.

Therefore, the three types of Spanish infinitives are word ends with -er , -ar, and -ir.

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the maximum volume of the swimming pool in cubic feet = 29744[tex]ft^{3}[/tex]

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder or a sphere.

Different shapes have different volumes. In 3D geometry, we have studied the various shapes and solids such as cubes, cuboids, cylinders, cones, etc., that are defined in three dimensions. For all these shapes, we are going to learn to find the volume.

Volume of a solid is measured in cubic units. For example, if dimensions are given in meters, then the volume will be in cubic meters. This is the standard unit of volume in the International System of Units (SI). Similarly, other units of volume are cubic centimeters, cubic feet, cubic inches, etc.

given that

the combined surface area of the floor of the pool and the four sides is $4800$ square feet.

each side (there are 4)   =  4   x w x w

and the bottom                     w x w              

 total surface area   5 w^2 = 4800

 w = depth = 30.984 ft

 volume= 30.984^3 = 29744.89[tex]ft^{3}[/tex]

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The required answer is fail to reject a null hypothesis.

What is Null hypothesis?

The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is feasible to determine the probability that the null hypothesis is correct using statistical testing.

Given that:

α = 0.05

then

z0.05 = 1.645

Hence, the rejection region is {z < −1.645}.

Hence, The required answer is fail to reject a null hypothesis.

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