Twenty-five households are surveyed and the number of children is recorded. The data is summarized in the frequency table below. Use the frequency table to compute the mean of the observations.

Answer:

-1/2, 5/3

Step-by-Step Explanation:

6z^2 - 7z - 5 = 0

=> 6z^2 - 10z + 3z - 5 = 0

=> 2z(3z - 5) + 1(3z - 5) = 0

=> (2z + 1)(3z - 5) = 0

=> z = -1/2, 5/3

Hope it helps.

If you have any query, feel free to ask.

Answer:

x = 14°

Step-by-step explanation:

We know that,

→ Straight line is always 180°.

Forming the equation,

→ 156° + (x + 10°) = 180°

Now the value of x will be,

→ 156° + (x + 10°) = 180°

→ x + 166° = 180°

→ x = 180° - 166°

→ [ x = 14° ]

Hence, the value of x is 14°.

The value of x in the given supplementary angle pair is 14°.

Then,

156 + (x + 10) = 180

166 + x = 180

x = 180 - 166

x = 14°

Thus, the value of x in the given supplementary angle pair is 14°.

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The inequality equation is x ≤ ( -12 )

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

( 1/4 )x  ≤  -3   be equation (1)

On simplifying the equation , we get

x/4 ≤ -3

Multiply by 4 on both sides of the equation , we get

x ≤ ( -3 ) ( 4 )

x ≤ -12

Therefore , the value of x is less than or equal to -12

Hence , the inequality equation is x ≤ -12

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According to definition of proportional ratios, 15 / 20 is not a multiple of 20 / 21.

In this problem we find two ratios in fraction form, both are proportional if the numerator and denominator of one of them are multiple of the corresponding elements of the other. First, write the fraction with the lowest numerator:

15 / 20

Second, multiply numerator and denominator by 4 / 3:

[15 · (4 / 3)] / [20 · (4 / 3)]

20 / 26.667

Ratio 15 / 20 is not proportional to ratio 20 / 21.

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10y⁶ is the width of the rectangle and y²+3 is the length of the rectangle.

The area of Rectangle is length times of width.

Given that the area of rectangle is 70y⁸+30y⁶

The width of the rectangle is the greatest common factor of 70y⁸ and 30y⁶

70y⁸+30y⁶

10y⁶(y²+3)

10y⁶ is the width of the rectangle.

y²+3 is the length of the rectangle.

Hence, 10y⁶ is the width of the rectangle and y²+3 is the length of the rectangle.

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Answer:

A) 234 feet

B) Area of new parking lot = 28080 square feet

C) The new parking lot will be able to fit 20 more cars than the original parking lot.

Step-by-step explanation:

We are given the following information:

Length of parking lot = 180 feet

Width of parking lot = 120 feet

Number of cars that can be parked = 75

A) Increase in length  = 30%

New length =

B) New area =

C) Space required by 1 car = 288 square feet

Number of cars we want to fit = 75 + 20 = 95

Area required =

Hence, the new parking lot will be able to fit 20 more cars than the original parking lot.

Answer:

-1/2

Step-by-step explanation:

slope is rise over run so find the difference between the y values (-9-(-5)) and divide that by the difference between the x values (-1-(-9)).

Answer: Total cup of flour=8 cups

One recipe calls for cup of flour=2/3

Cup of flour after making one recipe=8-2/3=(24-2)/3=22/3=7.33 cup of flour

Another recipe calls fro cup of flour=1/4

Cup of flour left after another recipe=22/3-1/4=(88-3)/12=85/12=7.08 cup of flour.

Amount of Floor left=7.08

Step-by-step explanation:

A measures magnitude 8 on the Richter scale of an earthquake is 10,000 times stronger than a magnitude 4 measure on the Richter scale.

Earthquake Intensity: An earthquake is the release of energy from the movement of tectonic plates. Earthquakes can be measured on the Richter scale, which ranges from 2 to 10 and measures the magnitude of an earthquake.

Earthquake intensity is a qualitative estimate of the effects caused by an earthquake, so it has no numerical value. The Richter scale is a logarithmic scale. This means that as you move up each digit, the power increases by a factor of 10. So let's set the damage from 4 earthquakes to X. Then, 5 = 10X

=> 6 = 100X

=> 7 = 1,000X

=> 8 = 10,000X

Hence, the required intensity is 10,000.

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Answer:

276.75

Step-by-step explanation:

one gallon lets sara drive 22.5 miles. multiply that by 12.3 and u get 276.75 !

Considering the definition of inequality, the inequality that can be used to determine x is 20x + 10 ≤ 80.

According to the question,

Addison wants to rent a car, we know that:

On the other hand, x denotes the maximum number of days. Alyssa can afford to rent while staying within her budget.

Then, the inequality that can be used to solve x is:

20x + 0.1×100≤ 80

so,

20x + 10≤ 80

Hence, the inequality which can be used to determine x is 20x + 10≤ 80.

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Answer: Look below

Step-by-step explanation:

Multiply the number in the one's place, Multiply the number in the ten's place and multiply the one's and ten's place with the hundred place number, then add them up.

Follow along with example 343 × 32:

Place one number above the other so that the ones' place digits and tens' place digits are lined up. Mark a line just below the bottom number.

 3 4 3

 ×3 2

_______

Multiply the ones' place digits (2 × 3 = 6), one's place of the second number by the ten's place of the first number (2 × 4 = 8), and one's place of the second number by the hundred place of the first number (2 × 3 = 6). Place the 6 below the line in the ones' place column, 8 below the line in the tens' place column and 6 below the line in the hundred place column.

3 4 3

×3 2

_________

6 8 6

Multiply the digit in the tens' place column (3) by the digit in the ones' place of the first number (3). The result is 3 × 3 = 9; multiply the digit in the tens' place column (3) by the digit in the tens' place of the first number (4). The outcome is 3 × 4 = 12, and multiply the digit in the tens' place column (3) by the digit in the hundred place of the first number (3). The outcome is 3 × 3 = 9. Now add the numbers and place the answer below the line.

3 4 3

×3 2

__________

   6 8 6

10 2 9×

__________

10 976

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An equation which represents the best model for a line of fit for the data is: y equals negative 2 thirds times x plus 7. The correct option is A.

A scatter plot should be used to determine a linear equation of the line of best fit (trend line) that models the data points described above.

In this scenario, the x-values would be plotted on the scatter plot's x-axis, while the y-values would be plotted on the scatter plot's y-axis.

Right-click on any data point on the scatter plot in Excel, select the format trend line, and then check the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between data points in the table, a linear equation for the line of best fit is given by:

y = -0.33x + 7.

Rewriting the equation as an improper fraction, we have:

y = -2/3(x) + 7

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Answer:

$33.75

Step-by-step explanation:

25% of 45 is 11.25 meaning you would get that much off as a discount making the shoes be $33.75

Check the picture below.

Answer: 65.65

Step-by-step explanation:

Carry over the decimals in each number.

2) Multiply. This will give you 6,565.

3) Carry the decimal place and count how many times you moved it over. (2=1+1) Therefore, it gives you 65.65

The total Social Security and Medicare taxes for the fourth quarter would be $728.00 ($600.00 for Social Security and $128.00 for Medicare). This is calculated by multiplying $5,000.00 by 12.4% for Social Security and 2.9% for Medicare.

The total Social Security and Medicare taxes for the fourth quarter would be $728.00. This is calculated by multiplying the total wages for the quarter ($5,000.00) by 12.4%, the Social Security tax rate for self-employed individuals, and then multiplying the same wages by 2.9%, the Medicare tax rate for self-employed individuals. This gives us $600.00 for Social Security taxes and $128.00 for Medicare taxes, for a total of $728.00. The Social Security tax rate is applied up to the wage base of $128,400 for the year.

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In the given figure, the length b is opposite the angle theta, and the length a is adjacent to the angle theta, so we can use the trigonometric ratios to express a and b in terms of theta:

What does trigonometry mean in plain English?

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

a = bsec(theta)

b = acosec(theta)

To evaluate sin(x+y), we can use the identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

sin(x+y) = sin(x)cos(y) + cos(x)sin(y)

We can use the given information to substitute the values of sin(x) and cos(y)

sin(x) = 1/3, cos(y) = sqrt(1 - (5/4)^2) = sqrt(9/16)

sin(x+y) = (1/3) * sqrt(9/16) + sqrt(9/16) * (1/3) = (3sqrt(9) + 9) / 48

To find all values of x such that sin 2x = sin x and 0 le x le 2pi, we can set sin 2x = sin x and solve for x.

sin 2x = sin x

2sinxcosx = sinx

cosx = 1/2

x = pi/3,5*pi/3

So the values of x that satisfy the equation are x = pi/3 and 5*pi/3

Note that these values are in radians, if you need in degree, x=60°, 300°

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Answer:

R' ( -2,1)

S' (-8,2)

T' ( -4,7)

Step-by-step explanation:

The measure of the exterior angle in this case is 60+60 = 120 degrees.

What is exterior angle ?

An exterior angle of a polygon is an angle formed between one side of the polygon and a line extended from the endpoint of the opposite side. An exterior angle can be formed by standing outside of the polygon and looking at it.

In a triangle, the measure of an exterior angle is equal to the sum of the measures of the two interior angles opposite to it. In any convex polygon, the sum of the measures of the exterior angles is always 360 degrees.

The support for a window air-conditioning unit forms a triangle. A triangle is a three-sided polygon, and all the interior angles in a triangle add up to 180 degrees. Therefore, the measure of each interior angle of a triangle is (180/3) = 60 degrees.

An exterior angle of a triangle is the angle formed between one side of the triangle and a line extended from the endpoint of the opposite side. In a triangle, the measure of an exterior angle is equal to the sum of the measures of the two interior angles opposite to it.

Therefore, the measure of the exterior angle in this case is 60+60 = 120 degrees.

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The value of x from the given figure is 12 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

Consider ΔADC and ΔABC,

∠C=∠C (Reflex property)

AC=AC (Reflex property)

∠BAC=∠CDA=90°

By AA similarity, ΔADC ~ ΔABC

So, AC/BC = DC/AC

x/36 = 4/x

x²=36×4

x²=144

x=12 units

Therefore, the value of x from the given figure is 12 units.

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Answer:

PSQ = x         since PSQ + 3 x = 4 x

So the triangle PQS is an equilateral triangle

2 x + y = 180       (y = PQS the angle opposite 68)

y + 68 = 180       these must add to 180

x = 34        subtracting the previous two equations

Answer:

No

Step-by-step explanation:

You must distribute 6 to BOTH numbers in the bracket

[tex]6(4b + 3d) = 24b + 18d[/tex]

Answer:

No, they are not equivalent !

Step-by-step explanation:

Simplify 6(4b + 3d)....

6(4b + 3d)

→ 6*4b+6*3d

→ 24b+18d

and we have....

→ 24b + 3d

So, no 6(4b + 3d) and 24b + 3d are not equivalent.

The equation for Tree A's height t years after being planted is:

[tex]A = 34 + 2t[/tex]

The equation for Tree B's height t years after being planted is:

[tex]B = 14 + 6t[/tex]

To determine the height of both trees at the time when they have an equal height, we can set the two equations equal to each other:

[tex]A = B[/tex]

[tex]34 + 2t = 14 + 6t[/tex]

And solving for t, we find that:

[tex]t = 10[/tex]

So, 10 years after being planted,

Tree A will be 54 inches tall  [tex](34 + 2 * 10)[/tex]  and Tree B will be 74 inches tall [tex](14 + 6 * 10)[/tex].

At this point, both trees will have an equal height.

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The Argument of 4 + 3i is arg(z) = 36.97◦.

Now, According to the question:

Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).

The standard format of a complex number is:

[tex]a +bi[/tex]

In which:

Given,

The complex number is:

z = 4 + 3i

We have to find the argument of the 4 + 3i.

The argument is given by:

θ = [tex]tan^-^1\frac{b}{a}[/tex]

tan θ = [tex]\frac{3}{4}[/tex]

θ = [tex]tan^-^1\frac{3}{4}[/tex]

θ = 36.97◦

The argument is θ = 36.97◦

We also have an abbreviation for argument: we write arg(z) = 36.97◦

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The inequality that represents the number of visits Tristan can make to earn his first free movie ticket is 8.5x + 25 ≥ 110.

In mathematics, an inequality is a relationship between two expressions or values that are not equal to each other.

In mathematics, there are five inequality symbols: greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).

Here,

Let us refer to x as the number of visits.

He receives 8.5 points for each visit,

That is he receives 8.5x points for x visits. i

Then there are the 25 reward points for simply signing up.

So the total points expression would be 8.5x + 25.

He needs at least 110 points to get a freebie,

Therefore the inequality is 8.5x + 25 ≥ 110.

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The perimeter of the horse corral is 600 feet.

The area of Rectangle is length times of width.

The area of any regular polygon is given by the formula: Area = (a x p)/2, where a is the length of the apothem and

p is the perimeter of the polygon.

Given that area of the horse corral is 3000 ft²

Length of the apothem is 10 ft

We need to find the perimeter.

3000=10p/2

6000=10p

Divide both sides by 10

600=perimeter

Hence, the perimeter of the horse corral is 600 feet.

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Answer:

[tex]\frac{4}{3}cm/s[/tex]

Step-by-step explanation:

By looking at the graph, we can use the slope formula.

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

We can substitute the point values into the equation.

[tex]\frac{16-0}{12-0}[/tex]

Then simplify.

[tex]\frac{16}{12}[/tex]

This fraction has the greatest common denominator of 4, so we will divide the numerator and the denominator.

[tex]\frac{16}{12}=\frac{4}{3}[/tex]

Therefore, the speed of the snail has a unit rate of [tex]\frac{4}{3} cm/s[/tex].

The distance formula can be used to prove that a triangle has congruent sides.

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