Which graphs correctly display the height data from the math class?
Responses
A box plot, dot plot, and histogrambox plot, dot plot, and histogram
B box plot and dot plot onlybox plot and dot plot only
C box plot and histogram onlybox plot and histogram only
D histogram and dot plot onlyhistogram and dot plot only
Question 2
Which graph displays can be used to find the median and the interquartile range of the data?
Responses
A box plot and dot plot onlybox plot and dot plot only
B histogram and dot plot onlyhistogram and dot plot only
C box plot and histogram onlybox plot and histogram only
D box plot, dot plot, and histogram

Answer:

5(-2m - 4) is equivalent to 10m + 20.

Answer:

D) 10m+20

Step-by-step explanation:

To solve for this, we have to solve -5(-2m-4).

To do this, distribute (multiply) -5 to both of the numbers in the parathesis:

-5x-2m

=10m

-5x-4

=20

10m+20

So, D is the correct answer.  Hope this helps :)

The commission percentage for the sales is 3%.

A mathematical statement known as an equation, typically with an equal sign, illustrates the relationship between two expressions. To determine the values of the variables that make an equation true, equations can be solved.

On the other hand, a function is a collection of ordered pairs where each input value (also known as the independent variable) and each output value (also known as the dependent variable) have a precise correspondence. Although equations are frequently used to write functions, this is only one approach to express a function.

Given, your commission percentage is x​.

Now, for commission x percent of the sales we have:

$140 = ($13 x 8) + (x/100 x $1200)

$140 = $104 + 12x

$36 = 12x

x = 3

Hence, the commission percentage for the sales is 3%.

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A graph titled "Monthly Sales and Advertising Costs" has advertising costs (1,000 dollars) on the x-axis and sales (1,000 dollars) on the y-axis. The line goes through points (6.4, 117) and (6.6, 120) with a slope of 15.

The slope of the trend line represents the rate of change of the data. In this case, the slope is positive, which means there is a positive correlation between advertising costs and sales. For every $1,000 increase in advertising costs, the sales increase by $15,000. So, the correct statements are:

1. The slope represents the rate of change of the data.
2. Sales increase $15,000 as ads increase by $1,000.
3. A positive slope infers a positive correlation.

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Step-by-step explanation:

volume = L x W x H

 180 ft^3  =  L x 6 x 6   ft

    180 / ( 6x6) = L = 5ft

Determining which plot element is the most challenging to write can pose difficulties for writers, largely depending on their individual style and the story they are crafting.

One of the more difficult plot elements can be the climax, which requires careful buildup and execution to deliver on achieving a satisfying payoff for readers due to escalating tensions throughout the narrative.

Writers tend to employ two common narrative approaches in their writing- dialogue and sensory details. Dialogue helps establish characters' drive, emotions, and motivations, while also advancing the plot and providing critical information to readers. Sensory details create immersive scenes with vivid imagery that allow readers to become invested into the story's ambiance and location.

In sum, by utilizing sensory details, authors capture readers' senses and render stories more tangible, while dialogue helps readers grasp characters' actions and feelings.

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Answer:

m = 3

Y-intercept: 75

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = Y-intercept

We see

m = 3

b = 75

So, the slope is 3 and the intercept is 75

The answer of the given question based on the Linear equations is , the slope of the line is 3 and the y-intercept is 75.

Slope is measure of  steepness of  line on a graph. It describes  rate at which  line rises or falls as it moves from left to right, and it is defined as  ratio of  vertical change (rise) to horizontal change (run) between any two points on  line.

In the equation y = 3x + 75, the coefficient of x is 3, which represents the slope of the line. Therefore, the slope of line is 3.

The equation is already in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. The y-intercept is value of y when x is 0. In this case, when x is 0, y is:

y = 3(0) + 75

y = 75

So the y-intercept of the line is 75.

Therefore, the slope of the line is 3 and the y-intercept is 75.

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The equation that belongs to the same function family as the graph shown below is given as follows:

C. h(x) = 2(5)^x.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The graphed function is a decreasing exponential function, belonging to the exponential function family.

Hence the correct option is given by option C, as it is the only exponential function among the options given.

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Answer:

Nicole bought 4 fancy shirts and 3 plain shirts.

Step-by-step explanation:

I multiplied 28 x 4 to get $112

then I multiplied 8 x 3 to get $24

You add $112 and $24 to get $136.

The value of measure of the smallest angle in this triangle is, 40 degree

Since,

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Here, The measure of three angles of triangle are given;

⇒ (x²+34)°, (6x+4)°, and (10x+10)°.

Hence,

(x²+34)°+(6x+4)°+(10x+10)°=180°

x²+16x+48=180

x²+16x-132=0

Using splitting middle term method, we get

x²+22x-6x-132=0

x(x+22)-6(x+22)=0

(x+22)(x-6)=0

x-6=0

x=6

Therefore, the value of of measure of the angle in this triangle is,

⇒ x² + 34 = 6² + 34 = 36 + 34 = 70

⇒ (6x + 4) = 6 × 6 + 4 = 40

⇒ (10x + 10) = 10 × 6 + 10 = 70°

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[tex]\sin( x )=\cfrac{\stackrel{opposite}{6}}{\underset{hypotenuse}{16}} \implies \sin( x )=\cfrac{3}{8}\implies x=\sin^{-1}\left( \cfrac{3}{8} \right)\implies \boxed{x\approx 22^o} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{16}\\ a=\stackrel{adjacent}{x}&\leftarrow \textit{Joel's shadow}\\ o=\stackrel{opposite}{6} \end{cases}[/tex]

[tex](16)^2= (x)^2 + (6)^2\implies \boxed{6^2+x^2=16^2}\implies x^2=16^2-6^2 \\\\\\ x=\sqrt{16^2-6^2}\implies x=\sqrt{220}\implies \boxed{x\approx 14.83}~ft[/tex]

Make sure your calculator is in Degree mode.

Answer:

square root of x.

If the area is "x" the length must be the square root of x because all sides of a square are equal and the square root of x times itself equals x

Using differentials, the approximate value of (4.99)³ is 124.25, and using a calculator, the value is 124.251.

To use differentials to approximate the value of the expression (4.99)3, we can use the formula:

Δy ≈ dy = f'(x)Δx

Where f'(x) is the derivative of the function f(x) = x3 evaluated at x = 5, since we are approximating around x = 5, and Δx is the change in x from 5 to 4.99, which is -0.01.

f'(x) = 3x2
f'(5) = 3(5)2 = 75

Δy ≈ dy = 75(-0.01) = -0.75

So, the approximate value of (4.99)3 using differentials is:

(4.99)3 ≈ (5 + Δx)3 ≈ 53 + 3(53)(-0.01) = 124.2575

Rounding to four decimal places, we get:

(4.99)3 ≈ 124.2575

Using a calculator, we get:

(4.99)3 = 124.251

Comparing the two values, we see that the approximation using differentials is very close to the value obtained using a calculator. The difference is only in the third decimal place, which is likely due to rounding errors in both calculations.

Step 1: Choose a base point
Since 4.99 is close to 5, we will choose 5 as our base point (x = 5).

Step 2: Find the expression's value at the base point
At x = 5, the expression is (5)³ = 125.

Step 3: Calculate the derivative of the expression
For the expression x³, the derivative is 3x².

Step 4: Find the derivative's value at the base point
At x = 5, the derivative is 3(5)² = 3(25) = 75.

Step 5: Calculate the differential
Δx = 4.99 - 5 = -0.01.

Step 6: Approximate using differentials
Δy ≈ dy = (derivative) * Δx = 75 * (-0.01) = -0.75.

Step 7: Add the differential to the base point value
Approximate value = 125 + (-0.75) = 124.25.

Now, let's compare this with a calculator result.

Using a calculator:
(4.99)³ ≈ 124.251

In conclusion:
Using differentials, the approximate value of (4.99)³ is 124.25, and using a calculator, the value is 124.251. Both values are rounded to four decimal places.

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The state income tax owed on a $70,000 per year salary is $ $3,684.

To compute the state income tax payable on a $70,000 per year wage, we must first estimate how much of the salary falls into each progressive tax band and then calculate the tax owed for each range.

The first $2,000 in earnings is taxed at 2%:

This portion's tax = $2,000 x 0.02 = $40

The following $7,000 in earnings (from $2,001 to $9,000) is taxed at 5%:

This portion's tax = $7,000 x 0.05 = $350

The remainder of your income beyond $9,000 is taxed at 5.4%:

This portion's tax = ($70,000 - $9,000) x 0.054

= $61,000  x 0.054

= $ 3294

Now, the total amount of tax owed = 40 + 350 + 3294

= $ 3,684.

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Correct question:

A certain state uses the following progressive tax rate for calculating individual income tax:

Income Range ($)          Progressive Tax Rate

0-2000                                   2%

2001-9000                               5%

9001 and up                         5.4%

Calculate the state income tax owed on a $70,000 per year salary.

tax = $[?]

Round your answer to the nearest whole dollar amount

It cost $8,428.80

The first step to solving this problem is to find the area of the deck in square yards. We can do this by multiplying the length by the width:

Area of the deck = Length x Width = 8 yards x 12 yards = 96 square yards

Next, we can find the total cost of building the deck by multiplying the area by the cost per square yard:

Total cost = Area of the deck x Cost per square yard

Total cost = 96 square yards x $87.85 per square yard

Total cost = $8,428.80

Therefore, it cost $8,428.80 to build Ryan's backyard deck.

The true statement is that D. On average, Rosalie scored higher on her maths test that Marvin.

Mean = (68+73+76+76+83+83+86)/7 = 77.14%

Therefore, this claim is untrue.

Rosaline's test results fall within a range of scores that is 11.

Q3 - Q1 = 16% is the interquartile range (IQR).

Therefore, this claim is untrue.

C) Marvin and Rosalie both had a wider range of test results.

The gap between the greatest and lowest scores is known as the range.

Range = 86 - 68 = 18% for Marvin.

Range = 97 - 70 = 27% for Rosalie

Therefore, this claim is untrue.

Rosalie performed better than Marvin on math exams on average.

Rosalie's test results' average were calculated as follows: Mean = (70+84+86+89+93+95+97)/7 = 87.14%

So, this assertion is accurate.

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The possible numbers of minutes Jim will run today is  represented by the inequality: 42 ≤ t ≤ 6x

If Jim runs at least 7 laps today, then the minimum number of minutes he will run is 7 laps x 6 minutes/lap = 42 minutes.

To find the maximum number of minutes he will run, we need to consider the possibility that he runs more than 7 laps.

Let's say he runs x laps in total, where x is greater than or equal to 7. Then the total number of minutes he will run is n laps x 6 minutes/lap = 6n minutes.

Therefore, the possible numbers of minutes Jim will run today can be represented by the inequality: 42 ≤ t ≤ 6x

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Part(a),

The amount added to the account each year will be £98.

Part(b),

After two years, there will be £1602.86 in the account.

a) Apply the basic interest formula to determine how much is added to the account annually:

I = Prt

where I stands for interest, P for principal, r for the interest rate expressed as a decimal per year, and t for the period of time in years.

P = £1400, r = 0.07, and t = 1 in this instance (since we are calculating the interest for one year). When these values are added to the formula, we obtain:

I = 1400 × 0.07 × 1 = £98

Therefore, £98 is added to the account each year.

b) The interest earned in the first year must be added to the principal to determine the balance in the account after two years, and the interest earned in the second year must be determined using the same formula:

Year 1: Interest = £98, Total amount = £1400 + £98 = £1498

Year 2: Interest = 1498 × 0.07 × 1 = £104.86, Total amount = £1498 + £104.86 = £1602.86

Therefore, after two years, there will be £1602.86 in the account.

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The classifications that must be the according to the figure are:

For RSUT

For XVWY

For ABCD

A rectangle is a four sided polygon otherwise known as a quadrilateral that has other properties such as

For ABCD, the third property mentioned here is failing as the diagonals are not equal.

Other figures makes us the desired properties of a rectangle

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On plotting the equation on the graph the value of x is -1.25. The correct option is C.

A function is a rule in mathematics that links every element of one set, known as the domain, with precisely one element of another set, known as the range.

A function is, to put it simply, a relationship between two sets of numbers in which each input (domain value) has exactly one corresponding output (range value).

One method is to graph both sides of the equation and find the point of intersection. We can graph y = -4x-1  [tex]y = 5^x+4[/tex] on the same set of axes. The point of intersection will give us an approximate solution.

When the graph is plotted on the x-y axis the value of the x coordinate will be -1.28. Which is approximately equal to -1.25.

Therefore, the value of x will be -1.25. The correct option is C.

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The volume of the composite figure is 123 cm³

From the image shown, we can see that the composite is made up of a cone and a rectangular prism.

The volume of a rectangular prism is expressed as;

V = lwh

Such that the parameters are;

Substitute the values

Volume, V = 5 × 1 × 12

Multiply the values

Volume = 60 cm³

The formula for the volume of a cone is expressed as;

Volume = πr²h/3

Substitute the values

Volume = 3 × 3² × 7/3

Multiply the values

Volume = 63 cm³

Then, the total volume = 63 + 60 = 123 cm³

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Answer:

C = (-3/2, 1)

r = 25

Step-by-step explanation:

4x² + 12x + 4y² - 8y = 87        divide both sides by 4

x² + 3x + y² - 2y = 87/4           rearrange the equation

(x² + 3x + h) + (y² - 2y + k) = 87/4 + h + k       complete the square

h = (3/2)² = 9/4

k = (-2/2)² = 1

(x² + 3x + 9/4) + (y² -2y + 1) = 87/4 + 9/4 + 1

(x² + 3x + 9/4) + (y² -2y + 1) = 25

(x + 3/2)² + (y - 1)² = 25

r² = 25

r = √25 = 5

C = (h, k) = (-3/2, 1)

The table of distance of points from the origin is:

Less than 13 units       Equals to 13 units        Greater than 13 units

          M                                  N, P                                Q, R

We know that in Cartesian Coordinate Plane, the distance between the point (a, b) and the origin (0, 0) is given by,

D = √(a² + b²)

Coordinates of Point M = (12, -5)

So the distance of the point M to the origin

= √(12² + (-5)²)

= √(144 + 25)

= √169

= 13 units

Coordinates of Point N = (6, 11)

So the distance of the point N to the origin

= √(6² + 11²)

= √(36 + 121)

= √157

= 12.53 units (approximated to two decimal places)

< 13 units

Coordinates of Point P = (-9, 9)

So the distance of the point P to the origin

= √((-9)² + 9²)

= √(81 + 81)

= √162

= 12.73 units (approximated to two decimal places)

< 13 units

Coordinates of Point Q = (10, 9)

So the distance of the point Q to the origin

= √(10² + 9²)

= √(100 + 81)

= √181

= 13.45 units (approximated to two decimal places)

> 13 units

Coordinates of Point R = (-1, -13)

So the distance of the point R to the origin

= √((-1)² + (-13)²)

= √(1 + 169)

= √170

= 13.04 units (approximated to two decimal places)

> 13 units

hence the table is,

Less than 13 units       Equals to 13 units        Greater than 13 units

          M                                  N, P                                Q, R

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Answer:

Triangle A is correct since 87° + 23° + 70° = 180°.

The ratio of the areas is 4:7.

If two trapezoids are similar, then their corresponding sides are proportional. The ratio of the corresponding diagonal is given as 1:7, so let us assume that the ratio of the corresponding bases is also 1:7.

Let the bases of the trapezoids be a and 7a, and let the heights be h1 and h2 respectively. We can use the formula for the area of a trapezoid, which is:

Area = (1/2) × (sum of bases) × height

The area of the larger trapezoid is:

A2 = (1/2) × (a + 7a) × h2 = 4a × h2

The area of the smaller trapezoid is:

A1 = (1/2) × (a + 7a) × h1 = 4a × h1

We know that the corresponding diagonal is in the ratio of 1:7, which means that the corresponding sides are also in the ratio of 1:7. This implies that the corresponding heights are in the same ratio, i.e., h1:h2 = 1:7.

Therefore, we can write h1 = (1/7)h2. Substituting this into the expression for A1, we get:

A1 = 4a × h1 = 4a × (1/7)h2 = (4/7)A2

So the ratio of the areas of the smaller trapezoid to the larger trapezoid is:

A1 : A2 = (4/7) : 1

Therefore, the ratio of the areas of the two similar trapezoids is 4:7.

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Answer:

Step-by-step explanation:

This is the difference of squares.  There is no GCF to take out.

The first term is a "perfect square" and so is the second term

You can take the square root of both terms perfectly

[tex]\sqrt{4w^{2} }[/tex] = 4w

√1 = 1

format for factors:

(√ of 1st term + √ of 2nd term)(√ of 1st term - √ of 2nd term)

The order of + and minus doesn't matter which parenthesis it goes in

factor:

(4w+1)(4w-1)

[tex]V = \pi(3)^2(21)[/tex] is the equation that shows the volume of the given cylinder.

The following formula may be used to determine a cylinder's volume:

[tex]V=\pi r^2h[/tex]

Where r is the radius of the cylinder's base, h is its height and is a mathematical constant that denotes the ratio of a circle's circumference to its diameter.

We must first determine the radius of the cylinder's base in order to utilize this formula to calculate the fulgurite's volume. The radius is equal to half of the base's diameter, or 3 inches since we know it to be 6 inches.

When we enter the values we are aware of into the formula, we obtain:

[tex]V = \pi(3)^2(21)[/tex]

Therefore, the expression that represents the volume is [tex]V = \pi(3)^2(21)[/tex]

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The compound inequality can be written as 83 ≤ x ≤ 91

we can write a compound inequality to represent this situation as:

83 ≤ (92 + 87 + 85 + 88 + 2x) / 6 ≤ 91

where x represents Marcus's score on the final exam (which counts as two tests).

To solve for x, we can start by multiplying both sides of the inequality by 6 to eliminate the denominator:

498 ≤ 352 + 2x ≤ 546

Next, we can subtract 352 from all sides of the inequality:

146 ≤ 2x ≤ 194

Finally, we can divide all sides of the inequality by 2:

73 ≤ x ≤ 97

Therefore, Marcus must score between 73 and 97 on his final exam to earn a "B" in the course.

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