What is the approximate area of the triangle below?

a)72.8 sq. cm.
b)111.9 sq. cm.
c)142.0 sq. cm.
d)164.7 sq. cm.

Step-by-step explanation:

Of the 1000 people randomly selected, 638 wear glasses.

638 / 1000 = 0.638

Since the sample is random, we can assume it is representative of the population.  So if there are 320 million people in the US, we would estimate the number that wears glasses is:

0.638 × 320 million ≈ 204 million

Answer:

204.16 million

Step-by-step explanation:

Remember that the sample is 1000 people.

Of those 1000 people we know that 762 wear corrective lenses. 638 of these people wear glasses.

The probability that a randomly selected person will wear glasses is:

[tex]P = \frac{638}{1000}\\\\P = 0.638[/tex]

Then, the expected number of people who wear glasses is:

[tex]N = 320 * P[/tex]

Where N is given in units of millions.

[tex]N = 320 * 0.638[/tex]

[tex]N = 204.16\ million[/tex]

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:

(10,6) is a positive and (-2, -3) are negative

Step-by-step explanation:

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.

Answer:

The length of a side of the base is 20 centimeters.

The area of a lateral side between the bases is about 126.5 square centimeters.

Step-by-step explanation:

It's a rectangular prism with a total volume of 800 cu cm, and a height of 20 cm.

So, the base has an area of...  800/20 = 40 sq cm.

The prism is a cube.   NO.  If it was a cube, the base would be 400 sq cm (20x20), since the height is 20.

The diagonal of the base is 4 centimeters. NO. with a base of 40 sq cm, it's impossible to have a diagonal of 4 cm.  A diagonal would form a hypotenuse... and an hypotenuse is longer than the two other sides... an hypotenuse of 4 would mean for example sides of about 2 and 3...  which gives 6 sq cm for the base, not 40.

The length of a side of the base is 20 centimeters.  COULD BE. The base is 40 sq cm, it could have a side of 20 and the other of 2.  Without knowing more about the prism than what's included in the question, we can't say YES and we can't say NO.

The area of a base is 40 square centimeters.  Yes

The area of a lateral side between the bases is about 126.5 square centimeters. YES, since the height is 20, that would mean one side of the base would be roughly 6.325 cm... for a base area of 6.325 x 6.325 = 40 sq cm.

1. The area of a base is 40 square centimeters.

2. The area of a lateral side between the bases is about 126.5 square centimeters.

The statements that describe the prism are:

1. The area of a base is 40 square centimeters.

To find the volume of any rectangular prism, we use the formula [tex]base \times height[/tex].

It is given that the volume of prism is 800 cubic centimeters and height is 20 centimeters.

Putting these values in the volume formula, to find base(B):

[tex]800=B(20)[/tex]

[tex]B=40[/tex]

Hence, area of base is 40 square centimeters.

2. The area of a lateral side between the bases is about 126.5 square centimeters.

Answer:

15/36 = 5/12 = 41.66%

Step-by-step explanation:

If a die is rolled twice in a row, and the up face value of both throws are added, that's basically like if you had thrown 2 dice at the same time.

If you throw 2 dice at the same time, there are 36 possible outcomes, from (1,1), (1,2)... to (6,5), (6,6).

You just then have to calculate how many combinations are greater than 7.  We have (2,6), (3,5), (3,6), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), (6,2), (6,3), (6,4), (6,5) and (6,6)... a total of 15 values above 7.

So, the probability is 15 totals  >7  out of 36 possible outcomes:

15/36 = 5/12 = 41.66%

Hello There!

All of the areas are indeed perfect squares.

4x4 is 16

5x5 is 25

3x3 is 9

Negative one is a natural number.

Answer:

c

Step-by-step explanation:

ANSWER

A. 12

EXPLANATION

From the stem-and-leaf plot, the trees that are between 610 inches tall and 640 inches tall are:

613,616,622,622,624,625,631,631,633,637,637,and 638.

Counting the number of trees gives 12 of them.

Therefore, the number of trees that are between 610 inches tall and 640 inches tall is 12.

The correct answer is A.

Range: [0, ∞), {y|0 ≤ y}

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:

Step-by-step explanation:

An angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

Therefore we have the equation:

[tex]\dfrac{x+8}{10}=\dfrac{2x-5}{14}[/tex]              cross multiply

[tex]14(x+8)=10(2x-5)[/tex]             use the distributive property

[tex](14)(x)+(14)(8)=(10)(2x)+(10)(-5)[/tex]

[tex]14x+112=20x-50[/tex]           subtract 112 from both sides

[tex]14x=20x-162[/tex]           subtract 20x from both sides

[tex]-6x=-162[/tex]         divide both sides by (-6)

[tex]x=27[/tex]

Answer:

27.

Step-by-step explanation:

I just did this question and I got it incorrect by answering 12. It's 27!

Answer:

(6,000 + 800 +20) /10

(60,000 + 8,000 + 200) / 100

682,000 / 1,000

Step-by-step explanation:

Use a calculator

Do the parenthesis first and divide

The division problems that result in a quotient of 682 are 682,000 ÷ 1,000 and 6,820,000 ÷ 10,000. This is because when we divide these large sums by their respective divisors, we get 682 as the quotient.

To figure out which division problems result in a quotient of 682, we need to remember how division works. Division is basically the opposite of multiplication - if you multiply the quotient by the divisor, you should get the dividend. Essentially, we're looking for problems where we divide a total (dividend) by a number (divisor) and get 682 (quotient).

For instance, if we were to have a division problem like 682,000 ÷ 1,000, we would get 682 as our quotient. The same would be true for 6,820,000 ÷ 10,000, where the quotient would also be 682.

However, the problems such as (600 + 80 + 2) ÷ 10, and (60,000 + 8,000 + 200) ÷ 100 do not result in a quotient of 682 and therefore don't apply. So only the two problems with the larger sums (682,000 ÷ 1,000 and 6,820,000 ÷ 10,000) are valid solutions.

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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.

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:

-2（x+5）= -2（x-2）+5

-2x-10=-2x+4+5

-2x+2x=-4+5+10

0=19

No solution

Answer:

no solution

Step-by-step explanation:

They are no = in any way, shape, or form

Please mark me brainlyest my friend i really need it

Answer:

$9.75

Step-by-step explanation:

Answer:

Step-by-step explanation: $9.75 per hour

243.75/25= 9.75

Answer:

x > 23

Step-by-step explanation:

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

You will get x > 23

Answer:

-5x+2y+1>0

Step-by-step explanation:

Plug in -2 for x and -1 for y. This is the only answer that gives you a positive number that is greater than zero.

Answer: Second Option

Step-by-step explanation:

Substitute the point in each of the given inequalities and verify if the inequality is met.

If the inequality is fulfilled then the point belongs to the region

For

[tex]5x-2y +1>0[/tex]

[tex]5(-2)-2(-1) +1>0[/tex]

[tex]-10+2 +1>0[/tex]

[tex]-7>0[/tex]

-7 is not greater than zero. the inequality is not met

For

[tex]-5x+2y +1>0[/tex]

[tex]-5(-2)+2(-1) +1>0[/tex]

[tex]10-2 +1>0[/tex]

[tex]9>0[/tex]

9 is greater than zero. So the point belongs to inequality

For

[tex]-2x+5y -1>0[/tex]

[tex]-2(-2)+5(-1) -1>0[/tex]

[tex]4-5-1>0[/tex]

[tex]-2>0[/tex]

-2 is not greater than zero. the inequality is not met

For

[tex]2x+5y -1>0[/tex]

[tex]2(-2)+5(-1) -1>0[/tex]

[tex]-4-5 -1>0[/tex]

[tex]-10>0[/tex]

-10 is not greater than zero. the inequality is not met

Answer:

(-3,4)

Step-by-step explanation:

The axis of symmetry, or X coordinate for a parabolic function is [tex]\frac{-b}{2a}[/tex]

By plugging in 6 for b, and 1 for a, you have -3.

By then plugging back into the function you can get the Y coordinate of the vertex.

[tex]f(x)=(-3)^{2}+6(-3)+13[/tex]

Or 4.

The answer is (-3,4)

ANSWER

(-3, 4)

EXPLANATION

The given function is

[tex]f(x) = {x}^{2} + 6x + 13[/tex]

We complete the square to obtain the vertex form:

We add and subtract the square of half the coefficient of x.

[tex]f(x) = {x}^{2} + 6x + {3}^{2} + 13 - {3}^{2} [/tex]

The first three terms form a perfect square trinomial.

[tex]f(x) = {(x + 3)}^{2} + 13 - 9[/tex]

[tex]f(x) = {(x + 3)}^{2} + 4[/tex]

Comparing this to the vertex form;

[tex]f(x) = {(x - h)}^{2} + k[/tex]

h=-3 and k=4

Answer:

Interior

Step-by-step explanation:

The sum of the interior angles of a polygol with n sides is 180(n-2)

Answer:

Interior

Step-by-step explanation:

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

Answer:

( ( 3(8) ) /2 ) - 7 = 5

Step-by-step explanation:

Eliminate the denominator by reducing the fraction by 2

3(4) - 7

Solve:

12 - 7

= 5

Answer:

5

Step-by-step explanation:

Given

[tex]\frac{3x}{2}[/tex] - 7

To evaluate substitute x = 8 into the expression

[tex]\frac{3(8)}{2}[/tex] - 7 = [tex]\frac{24}{2}[/tex] - 7 = 12 - 7 = 5

Answer:

B.  50 km/hr

Step-by-step explanation:

speed of train relative to man = [tex]\frac{125}{10}[/tex] m/sec

= [tex]\frac{25}{2}[/tex] m/sec

= ([tex]\frac{25}{2}[/tex] x [tex]\frac{18}{5}[/tex] ) km/hr

= 45 km/hr

let the speed of the train be x km/hr (x=-5)

x -5 = 45

x -5 + 5 = 45 + 5

x = 50 km/hr

Answer:

50 km/hr.

B

Step-by-step explanation:

I get the same answer (50 km/hour) but I did it slightly differently and both solutions are worth seeing.

First of all you have to figure out how far the man runs. Assume he starts right at the tip of the cow catcher (the furthest point out on one of those old fashioned engines.

He runs at 5km / hour for 10 seconds.

5 km = 5000 meters.

5000 meters / hour * [1 hour / 3600 seconds ] = 1.38889 m/sec.

He does this for 10 seconds

d = r * t

d = 1.38889 * 10

d = 13.8889

Now look at what the train has to do. It passes him in 10 seconds. (The train has gone from the tip of the cow catcher to the end of the caboose in 10 seconds.)

d = 125 + 13.8889 meters

d = 138.8889 meters.

Now we have to convert this to km / hour

138.8889 m / 10 seconds [ 1 km/ 1000 m] *  [ 3600 sec / 1 hr.]

(138.8889 * 1 * 3600 ) / (10 * 1000 * 1 )

50.000004

So the answer is 50 km/hr.

Answer:

one x-intercept.

Transformation: shift to the right 8 units.

Step-by-step explanation:

The parent function is [tex]f(t)=t^{2}[/tex]

To find the number of x-intercepts, we equate the function to zero.

[tex]\implies t^{2}=0[/tex]

[tex]\implies t=0[/tex]

There is only one x-intercept at t=0.

The transformed function is

[tex]g(t)=(t-8)^2[/tex]

This function is obtained shifting the parent function 8 units to the right.

The x-intercept will now be at t=8.

Hence the image function also has one x-intercept.

Answer:

2. Given

3. Definition of supplementary angles

4. Substitution Property

5 Subtraction Property

Step-by-step explanation:

2. Given

We are given in the statement that m<1 = 112°

3. Definition of supplementary angles

Supplementary angles definition: Two angles are supplementary if there sum is equal to 180°. That statement states:

m<1 + m<2 = 180°

4. Substitution Property

We put the value of m<1 = 112° in the equation. This is substitution property.

5. Subtraction Property

To find the value of m<2 we subtract 112 from both sides of the equation.

This is subtraction property.

Answer:

. from line l. In a coordinate plane, the locus of points 5 units ... 30. * .. ... The distance between parallel lines 6 and m is 12 units. Point A is on ...

Step-by-step explanation:

Answer:

(3z - 1)(z + 9)

Step-by-step explanation:

Answer:

(z + 9)(3z - 1)

Step-by-step explanation:

Given

3z² + 26z - 9

To factor the quadratic

Consider the factors of the product of the z² term and the constant term which sum to give the coefficient of the z- term

product = 3 × - 9 = - 27 and sum = + 26

The factors are + 27 and - 1

Use these factors to split the z- term

3z² + 27z - z - 9 ( factor the first/second and third/fourth terms )

3z(z + 9) - 1(z + 9) ← factor out (z + 9) from each term

(z + 9)(3z - 1) ← in factored form

Answer:

from sloping up to sloping down ⇒ answer D

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

 function g(x) = f(-x)

* Now lets solve the problem

∵ The equation of the line is y = 2x - 6

∵ The equation is changed to y = -2x - 6

- If the both signs of x and the number are changed means the

 equation is multiplied by -1

∴ The line is reflected across the x-axis

- If the sign of x only is changed

∴ The line is reflected across the y-axis

- From the equation 2x changed to -2x, but -6 not changed

∴ The sign of x only changed

∴ The line is reflected across the y-axis

* The graph is reflected across the y-axis

∴ from sloping up to sloping down

The line is reflected over the x axis

[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\[2em] \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ \cline{2-4}&\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\[-0.35em] ~\dotfill \\\\ \cfrac{\textit{small polygon}}{\textit{large polygon}}\qquad \qquad \cfrac{3}{9}\implies \cfrac{1}{3}\implies \stackrel{ratio}{1:3}[/tex]