Find the range for the set of data.


101, 72, 115, 114, 117, 56, 101, 68, 111, 58, 51, 51, 90

Answer:

[tex]\large\boxed{y-intercept=20}[/tex]

Step-by-step explanation:

[tex]\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ y=\dfrac{3}{5}x+10\to m_1=\dfrac{3}{5}.\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{3}{5}}=-\dfrac{5}{3}.\\\\\text{The equation of the searched line:}\ y=-\dfrac{5}{3}x+b.\\\\\text{The line passes through }(15,\ -5).[/tex]

[tex]\text{Put thecoordinates of the point to the equation.}\ x=15,\ y=-5:\\\\-5=-\dfrac{5}{3}(15)+b\\\\-5=(-5)(5)+b\\\\-5=-25+b\qquad\text{add 25 to both sides}\\\\b=20\\\\\boxed{y=-\dfrac{5}{3}x+20}[/tex]

ANSWER

(C) d=1

EXPLANATION

The given equation is

[tex] \frac{ - 3d}{ {d}^{2} - 2d - 8} + \frac{3}{d - 4} = \frac{ - 2}{d + 2} [/tex]

Factor the first fraction to get,

[tex] \frac{ - 3d}{(d + 2)(d - 4)} + \frac{3}{d - 4} = \frac{ - 2}{d + 2} [/tex]

Multiply through by (d+2)(d-4)

[tex] - 3d + 3(d + 2) = - 2(d - 4)[/tex]

Expand:

[tex] - 3d + 3d + 6 = - 2d + 8[/tex]

[tex] 6 = - 2d + 8[/tex]

[tex]6 - 8= - 2d[/tex]

[tex] - 2 = - 2d[/tex]

divide both sides by -2

[tex]d = 1[/tex]

The correct answer is (B) [tex]\( d = -2 \)[/tex] and [tex]\( d = 4 \)[/tex].

To find the solution to the given quadratic equation, we can factor it or use the quadratic formula. The equation is not provided in the conversation, but based on the options given, it seems that the equation could be in the form [tex]\( (d - a)(d - b) = 0 \)[/tex], where [tex]a[/tex] and [tex]b[/tex]are the roots of the equation.

The quadratic equation can be written as [tex]\( d^2 - (a+b)d + ab = 0 \)[/tex]. To have the sum of the roots [tex]\( a + b \)[/tex] equal to 0 and the product of the roots [tex]\( ab \)[/tex] equal to -8, we can set up the following system of equations:

1. [tex]\( a + b = 0 \)[/tex]

2. [tex]\( ab = -8 \)[/tex]

From equation 1, we can express [tex]\( b \)[/tex] in terms of [tex]\( a \): \( b = -a \).[/tex]

Substituting [tex]\( b \)[/tex] into equation 2, we get:

[tex]\( a(-a) = -8 \)[/tex]

[tex]\( -a^2 = -8 \)[/tex]

[tex]\( a^2 = 8 \)[/tex]

Taking the square root of both sides, we find:

[tex]\( a = \pm\sqrt{8} \)[/tex]

[tex]\( a = \pm2\sqrt{2} \)[/tex]

Since [tex]\( b = -a \),[/tex] we have:

[tex]\( a = 2\sqrt{2} \) and \( b = -2\sqrt{2} \)[/tex]

[tex]\( a = -2\sqrt{2} \) and \( b = 2\sqrt{2} \)[/tex]

However, these are not the exact values given in the options. We need to find the exact integer values for [tex]a[/tex] and [tex]b[/tex]. Since the product [tex]\( ab \)[/tex] is -8, we can look for two numbers that multiply to -8 and add up to 0. These numbers are -2 and 4.

Therefore, the solutions to the equation are [tex]\( d = -2 \)[/tex] and [tex]\( d = 4 \)[/tex], which corresponds to option (B).

Answer:

8y^50

Step-by-step explanation:

Answer:

8y^50

Step-by-step explanation:

Answer:

(b)

5 cm

5 cm

108

cm

1080

1080

5 cm

5 cm

108°

1089

5 cm​

Step-by-step explanation:

Ummmmm. :)

well hope it helped you!

Answer:

Given that ΔJKL ≅ ΔUVW and ΔUVW ≅ ΔABC, complete the following statements.

Triangle JKL is congruent to triangle .

Side LK corresponds to sides .

Angle JLK corresponds to angles .

Step-by-step explanation:

Answer:

x > 23

Step-by-step explanation:

Subtract 7 on both sides in the equation: x + 7 > 30

You will get x > 23

let's take a peek

we really have a rectangular prism below a square pyramid.

the prism has a front, back, left and right of a rectangle 2x11 .

its bottom or base is an 11x11 square.

the pyramid 4 triangles, each one has a base of 11 and a height of 7.

[tex]\bf \stackrel{\textit{front, back, left, right}}{4(2\cdot 11)}~~+~~\stackrel{\textit{base}}{(11\cdot 11)}~~+~~\stackrel{\textit{four triangles}}{4\left[ \cfrac{1}{2}(11)(7) \right]} \\\\\\ 88+121+154\implies 363[/tex]

Answer:

The surface area of composite solid = 363 ft²

Step-by-step explanation:

Points to remember

Area of rectangle = Length * Breadth

Area of triangle = bh/2

Where b - Base and h - Height

To find the surface area of composite solid

Surface area = Base area  + side area  + area of 4 triangles

 = (11 * 11) + 4(11 * 2) + 4(11 * 7)/2

 = 121 + 88 + 154

 = 363 ft²

Therefore the surface area of composite solid = 363 ft²

500/4 = x/1

125 = x

125 miles per inch.

The question from 'Middle School Math with Pizzazz! Book E' appears to utilize pie as a topic to explore fractions. It illustrates fractions visually, such as expressing three out of five slices of pie as 3/5, or six out of ten slices as 6/10 (which simplifies to 3/5).

The question seems to be from the 'Middle School Math with Pizzazz! Book E'. It doesn’t seem to relate directly to the creation of a vegetable necklace, but I can infer that it relates to the concept of fractions, as suggested in the information. In mathematical terms, the slicing of pies and selection of pieces can be equated to the division of a whole into smaller parts, which is how fractions are defined.

For example, slicing one pie into five slices and taking three of them can be represented as 3/5, or three-fifths.  This represents the concept of fractions in an easy-to-understand, visual way. Similarly, splitting one pie into 10 pieces and selecting 6 can be expressed as 6/10, or six-tenths, which also reduces to three-fifths when simplified.

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Final answer:

The 'vegetable necklace' problem seems to be a math-related craft activity aimed at teaching fractions or ratios. It involves creating a necklace pattern with vegetables in a consistent ratio, providing a hands-on way to understand these mathematical concepts in middle school math.

Explanation:

The question appears to be from a workbook called Middle School Math With Pizzazz! Book E, which suggests that the problem is related to a math puzzle or activity. Although the question mentions making a vegetable necklace, this is likely a math-based craft or theoretically presented problem for representing fractions, ratios, or patterns that are common in middle school mathematics.

Based on the provided reference (A.1), we can understand that this problem might be connected to fractions or proportional reasoning. The example given explains how we can divide pies into slices to represent different fractions yet end up with the same quantity. This principle can be applied to making a necklace, where vegetables represent parts of a whole, and different combinations can result in a necklace of the same length or number of items.

To make a vegetable necklace, a student could take a string and add vegetables at regular intervals, ensuring that the pattern or ratio remains consistent. For instance, if the pattern is one carrot for every two tomatoes, and the length of the necklace is to have 15 vegetables, there would be 5 carrots and 10 tomatoes on the string, maintaining the ratio.

This activity would give them a tangible representation of fractions and ratios, providing a hands-on experience in understanding these mathematical concepts.

Answer:

-3

Step-by-step explanation:

The x-intercept is the plot point where y = 0.

Answer:

-3

Step-by-step explanation:

the x-intercept is the point on the graph where the ploted line crosses the x axes  

Answer:

x=-2 is the only solution

Step-by-step explanation:

The given equation is

[tex]\sqrt{x+6}-4=x[/tex]

Add 4 to both sides of the equation.

[tex]\sqrt{x+6}=x+4[/tex]

Square both sides

[tex]x+6=(x+4)^2[/tex]

[tex]x+6=x^2+8x+16[/tex]

Rewrite in standard form;

[tex]x^2+8x-x+16-6=0[/tex]

[tex]x^2+7x+10=0[/tex]

[tex]x^2+7x+10=0[/tex]

[tex](x+2)(x+5)=0[/tex]

x=-2 or x=-5

Checking for extraneous solution.

When x=-2

[tex]\sqrt{-2+6}-4=-2[/tex]

[tex]\sqrt{4}-4=-2[/tex]

[tex]2-4=-2[/tex]. This statement is true. This implies that: x=-2 is a solution.

When x=-5

[tex]\sqrt{-5+6}-4=-5[/tex]

[tex]\sqrt{1}-4=-5[/tex]

[tex]1-4=-5[/tex]. This statement is not true. This implies that: x=-5 is an extranous solution.

Hello There!

All of the areas are indeed perfect squares.

4x4 is 16

5x5 is 25

3x3 is 9

The ratio is 5:8 campers

Answer:

50

--- Ratio: 50:80

80

Step-by-step explanation:

50 would be how many girls were that the summer camp. And the 80 is how many students all together at the summer camp.

Hoped This Helped You

Have A Wonderful day

The x - determinant of the equation is [tex]\left[\begin{array}{cc}0&-1\\-3&1\\\end{array}\right][/tex]

The y - determinant of the equation is [tex]\left[\begin{array}{cc}2&0\\1&-3\\\end{array}\right][/tex]

The system determinant is [tex]\left[\begin{array}{cc}2&-1\\1&1\\\end{array}\right][/tex]

How to find the determinants of x, y and the entire system?

The given system of equation include the following;

2x - y = 0

x + y = - 3

The x - determinant of the equation will be obtained by replacing coefficient of x with the constant terms.

[tex]\Delta x = \left[\begin{array}{cc}0&-1\\-3&1\\\end{array}\right][/tex]

The y - determinant of the equation will be obtained by replacing coefficient of y with the constant terms.

[tex]\Delta y = \left[\begin{array}{cc}2&0\\1&-3\\\end{array}\right][/tex]

The system determinant is obtained by removing the constant term and writing only the x and y coefficient in the matrix;

[tex]\Delta = \left[\begin{array}{cc}2&-1\\1&1\\\end{array}\right][/tex]

Answer:

C

Step-by-step explanation:

Answer:

The correct option is 3.

Step-by-step explanation:

The difference of squares is defined as

[tex]a^2-b^2=(a-b)(a+b)[/tex]

In option 1,

[tex](-7x+4)(-7x+4)=(-7x+4)^2[/tex]

This expression is a perfect square, therefore this is not the difference of squares. Option 1 is incorrect.

In option 2,

[tex](-7x+4)(4-7x)=(-7x+4)(-7x+4)=(-7x+4)^2[/tex]

This expression is a perfect square, therefore this is not the difference of squares. Option 2 is incorrect.

In option 3,

[tex](-7x+4)(-7x-4)=(-7x)^2-(4)^2[/tex]

This expression is the difference of squares., therefore Option 3 is correct.

In option 4,

[tex](-7x+4)(7x-4)=-(-7x+4)(-7x+4)=-(-7x+4)^2[/tex]

This expression is a perfect square, therefore this is not the difference of squares. Option 4 is incorrect.

Answer:

-30x+35

Step-by-step explanation:

Add 11 and 24

Answer:

720 in³

Step-by-step explanation:

The volume (V) of a right prism is calculated as

V = area of triangular end × length

area of Δ = [tex]\frac{1}{2}[/tex] bh

where b is the base and h the perpendicular height

here b = 8 and h = 15, thus

area of Δ = 0.5 × 8 × 15 = 4 × 15 = 60 in²

The length of the prism is 12 in, hence

V = 60 × 12 = 720 in³

B is the correct answer

Answer:

any score that lies between 88.8 and 97.2 is within one std. dev. of the mean

Step-by-step explanation:

One std. dev. above the mean would be 93 + 4.2, or 97.2.  One std. dev. below the mean would be 93 - 4.2, or 88.8.

So:  any score that lies between 88.8 and 97.2 is within one std. dev. of the mean.

The scores that fall within one standard deviation of the mean are between 88.8 and 97.2. This matches the last option provided.

The Empirical Rule helps us understand how data is distributed in a normal distribution. The rule states that approximately 68% of the data falls within one standard deviation of the mean.

Given a mean (μ) of 93 and a standard deviation (σ) of 4.2, we calculate the range within one standard deviation:

Therefore, the scores that fall within one standard deviation of the mean are between 88.8 and 97.2, which matches the last option.

Answer:

0

Step-by-step explanation:

Between -6 and 9 are 15 units.

2/5 of 15 units is 6 units.  Add this to -6 to obtain 0.

0 is the answer to this question

Step-by-step explanation:

I'm not sure but I think its like the distance between -6 and 9 is 15 or something and 15 divided by 5 is 3 and 2/5 is 6 so 6-6 is 0 and that's that point.

Answer:

[tex]\left(s\cdot t\right)\left(x\right)=2x^2+12x+16[/tex]

[tex]\left(s-t\right)\left(x\right)=-x[/tex]

[tex]\left(s+t\right)\left(4\right)=20[/tex]

Step-by-step explanation:

Given functions are:

[tex]s\left(x\right)=x+4[/tex]

[tex]t\left(x\right)=2x+4[/tex]

Then [tex]\left(s\cdot t\right)\left(x\right)=s\left(x\right)\cdot t\left(x\right)[/tex]

or [tex]\left(s\cdot t\right)\left(x\right)=\left(x+4\right)\left(2x+4\right)[/tex]

or [tex]\left(s\cdot t\right)\left(x\right)=2x^2+4x+8x+16[/tex]

or [tex]\left(s\cdot t\right)\left(x\right)=2x^2+12x+16[/tex]

---------

Similarly

[tex]\left(s-t\right)\left(x\right)=s\left(x\right)-t\left(x\right)[/tex]

or [tex]\left(s-t\right)\left(x\right)=\left(x+4\right)-\left(2x+4\right)=x+4-2x-4[/tex]

or [tex]\left(s-t\right)\left(x\right)=-x[/tex]

---------

Similarly

[tex]\left(s+t\right)\left(4\right)=s\left(4\right)+t\left(4\right)=\left(4+4\right)+\left(2\left(4\right)+4\right)=\left(8\right)+\left(12\right)=20[/tex]

[tex]\left(s+t\right)\left(4\right)=20[/tex]

Answer:

(1,2)

Step-by-step explanation:

I just used a graphing calculator

Answer:

48

Step-by-step explanation:

48 heads =48sheep. .i guess. .......

Something's odd with this question: each sheep has one head, so if you see 48 heads there are 48 sheeps.

But each sheep has also 4 legs, so if you have 48 sheeps you should see

[tex]48\cdot 4 = 192\text{ legs}[/tex]

So, unless you have some sheeps with missing legs, there must be a mistake in the question.

Answer:

[tex]-\sqrt{11}[/tex]

Step-by-step explanation:

As square root value is written with both + and - signs

In Given case:

A polynomial has root [tex]\sqrt{11}[/tex]

= ±3.316

Also [tex]-\sqrt{11}[/tex]

= ±3.316

Hence [tex]-\sqrt{11}[/tex] is also root of the polynomial!

The final answer is 16

The act or process of taking one number away from another is called subtraction.

According to the problem,

This can be written as (5 x 3) + 10- 9

 =  16

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Answer:

the correct answer is BCA

Answer:

The correct option is 2.

Step-by-step explanation:

Given information: [tex]m\angle 1=110^{\circ}[/tex].

It is given that [tex]m\angle 1=110^{\circ}[/tex], so arc(BA)=110° and the central angle of arc BCA is

[tex]Arc(BCA)=360^{\circ}-Arc(BA)[/tex]

[tex]Arc(BCA)=360^{\circ}-110^{\circ}[/tex]

[tex]Arc(BCA)=250^{\circ}[/tex]

The measure of arc BC is

[tex]180^{\circ}-110^{\circ}=70^{\circ}[/tex]

The measure of arc CTA is 180° because AC is the diameter.

It means options 1 and 3 are incorrect.

The measure of arc BCA is 250°. Therefore the correct option is 2.

Step-by-step explanation:

If you lost "y" in the first equation.

[tex]\underline{+\left\{\begin{array}{ccc}2x-3y=14\\-x+3y=-6\end{array}\right}\qquad\text{add both sides of the equations}\\\\.\qquad x=8\\\\\text{Put the value of x to the first equation:}\\\\2(8)-3y=14\\16-3y=14\qquad\text{subtract 16 from both sides}\\-3y=-2\qquad\text{divide both sides by (-3)}\\y=\dfrac{2}{3}\\\boxed{x=8,\ y=\dfrac{2}{3}}[/tex]

If first equation is correct.

[tex]2x-3=14\qquad\text{add 3 to both sides}\\2x=17\qquad\text{divide both sides by 2}\\x=8.5\\\\\text{Put the value of x to the second equation:}\\-8.5+3y=-6\qquad\text{add 8.5 to both sides}\\3y=2.5\qquad\text{divide both sides by 3}\\y=\dfrac{2.5}{3}\\y=\dfrac{25}{30}\\y=\dfrac{5}{6}\\\\\boxed{x=8.5,\ y=\dfrac{5}{6}}[/tex]

Answer:

[tex]\boxed{\text{(6, 3)}}[/tex]

Step-by-step explanation:

The conic form of the equation for a sideways parabola is

(y - k)² = 4p(x - h)

The focus is at (h + p, k)

The equation of Samara's parabola is

(y - 3)² = 8(x - 4)

h = 4

p = 8/4 = 2

k = 3

h + p = 6

So, the focus point of the satellite dish is at

[tex]\boxed{\textbf{(6, 3)}}[/tex]

Answer: This is some information I have gathered to help you since I cannot answer this directly sin θ + (cot θ)(cos θ)  

= sin θ + (cos θ / sin θ)(cos θ)  

= sin θ + cos² θ / sin θ  

Since cos² θ = 1 - sin² θ,  

= sin θ + (1 - sin² θ) / sin θ  

= sin θ + 1 / sin θ - sin θ  

= 1 / sin θ  

= csc θ ∎ Sin(x) = tan(x) / [sqrt(1 + tan^2(x)]  

Sin(theta) =3/4 / sqrt[1 + .75^2]

Sin(theta) =0.75 / sqrt[ 1.5625 ]

Sin(theta) =0.75 / 1.25

Sin(theta) = 0.60

That would be week 2 and 4 (B). They are both at 12 students attending

Hope this helped!

Answer:

The correct option is B.  weeks 2 and 4.

Step-by-step explanation:

Consider the provided histogram.

The histogram shows the weekly attendance of participants in a school's study skills program.

Now, consider the Histogram.

In week 1 the Student attendance was 8.

In week 2 the Student attendance was 12.

In week 3 the Student attendance was 15.

In week 4 the Student attendance was 12.

In week 5 the Student attendance was 18.

In week 6 the Student attendance was 16.

Hence the Student attendance numbers were the same during week 2 and week 4 of the workshop.

Therefore, the correct option is B.  weeks 2 and 4

Answer:

a) 3,6,9,12,15,..

b) Common Ratio is 3

c) Recursive Formula : aₙ= aₙ₋₁ + d where a₁=3 and d= 3

Step-by-step explanation:

a) Create your own arithmetic sequence. Write out the first 3 terms.

Consider the sequence: 3,6,9,12,15,..

a₁ = 3

a₂ = 6

a₃ = 9

b) What is the common difference of your sequence?

6-3 = 3

9-6 = 3

12 -9 =3

So, common difference is 3

c) Write the recursive formula representing your sequence.

a₁ = 3

a₂ = aₙ₋₁ + d

   = a₁ + d

   = 3+ 3 = 6

a₃ = aₙ₋₁ + d

    = a₂ + d

   = 6+3 = 9

so, recursive formula is aₙ = aₙ₋₁ + d where a₁ = 3 and d= 3

An example of an arithmetic sequence can be created with a starting value (a1) of 2 and a common difference (d) of 3. The sequence's terms would be 2, 5, 8, etc. Its recursive formula would be a1 = 2; a_n = a_(n–1) + 3.

Let's create an arithmetic sequence, starting with the first term (a1) of 2 and a common difference (d) of 3. So, the first three terms of the sequence would be 2, 2+3=5, and 5+3=8.

The common difference of this arithmetic sequence is 3 as each term is 3 greater than the previous term.

The recursive formula for this sequence is a1 = 2; a_n = a_(n–1) + 3. What this formula means is that the first term is 2, and each subsequent term (an) is the previous term (an-1) added to the common difference (3).

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