8. The Oklahoma Museum of Natural History claims that on average, a square foot of grass contains 3.1 x 10^3 blades of grass. The soccer field has an area of 1.148 x 10^5 square feet. How many blades of grass are on the entire soccer field?​

Answer:

Exponential

Step-by-step explanation:

By visual inspection the graph generated by the points plotted is an exponential graph as the graph curves upward. The graph is also continous and differs from either a decreasing or increasing Linear graph, which shows a straight best of fit pattern. Hence, the graph most closely represents an exponential graph from visual examination.

The best-fitting regression model for the considered data plot is given by:

Option A: Exponential.

When the data shows some trend, either linear (making a line), or non-linear (a predictable curve), we fit a mathematical curve on that data set, as a representative of the pattern in that data set, to predict the output based on the inputs.

The considered plot is not forming a straight line(so no linear fitting), but we can see that a smooth curve can be fitted in the considered data. Since the exponential functions' graph approximately goes the same way (for positive exponent, and increasing value of output).

Thus, the best-fitting regression model for the considered data plot is given by: Option A: Exponential.

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Answer:

Substitute your answer for Step 1 into the second equation to solve for Z.

Answer:

mean = 5

median = 4.5

mode = 4

Step-by-step explanation:

Mean :

n = 8

sum of all items = 4+6+5+4+4+5+4+8

= 10+9+9+12

= 19+ 21

= 40

so,

mean = sum of all items/ n

= 40/8

= 5

mean = 5

Median:

ascending order: 4,4,4,4,5,5,6,8

n = 8

md = (n+1)/2 the term

= (8+1)/2 th term

= 9/2 th term

= 4.5 th term

= (4th + 5th) / 2

= (4+5)/2

= 9/2

= 4.5

median = 4.5

x. f.

4. 4

5. 2

6. 1

8. 1

here the highest frequency is 4 and 4 is corresponding to 4

so, mode = 4

Answer:

no solution

Step-by-step explanation:

y = x+1 and y = x + 2 don't touch because they are parallel

if you don't know what parallel means, just search it up, but i can explain it to you:

parallel means same slope or same steepness of line

Answer:

B. 2.618 units

Step-by-step explanation:

the arc length = (5π/6) / 2π × 2×3.14×1

= 5/12 × 6.28

= 31.4/ 12

= 2.618 units

The arc length is = 2.618 units

Arc measure is a degree measurement, equal to the central angle that forms the intercepted arc. Arc length is a fraction of the circumference of the circle.

Given : r=1, [tex]\theta[/tex]= 5π/6

Now, arc length

= [tex]\theta[/tex]/ 2π * 2πr

= (5π/6) / 2π × 2×3.14×1

= 5/12 × 6.28

= 31.4/ 12

= 2.618 units

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Answer:

second option is correct

Answer:

[tex]\text{A. }\frac{4\sqrt{14}}{{7}}[/tex]

Step-by-step explanation:

In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side. Therefore, we can form a right triangle with non-right angle [tex]\theta[/tex] and its opposite side [tex]\sqrt{7}[/tex] and its adjacent side [tex]5[/tex].

By definition, [tex]\csc \theta=\frac{1}{\sin\theta}[/tex].

In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle. To find the hypotenuse, use the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or longest side, of the right triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle.

Solving, we get:

[tex]5^2+\sqrt{7}^2=c^2,\\25+7=c^2,\\c^2=32,\\c=\sqrt{32}=4\sqrt{2}[/tex]

Therefore, we have:

[tex]\csc \theta = \frac{1}{\sin \theta}=\frac{1}{\frac{\sqrt{7}}{4\sqrt{2}}},\\\\\csc \theta=1\cdot \frac{4\sqrt{2}}{\sqrt{7}},\\\\\csc \theta =\frac{4\sqrt{2}}{\sqrt{7}}\cdot \frac{\sqrt{7}}{\sqrt{7}}=\boxed{\text{A. }\frac{4\sqrt{14}}{{7}}}[/tex]

Answer: Choice A)   [tex]\frac{4\sqrt{14}}{7}[/tex]

======================================================

Explanation:

Refer to the figure below. We start off drawing a right triangle that has opposite side sqrt(7) and adjacent side 5.

This is because tan = opposite/adjacent.

Use the pythagorean theorem to find the hypotenuse is sqrt(32) which simplifies like so

sqrt(32) = sqrt(16*2) = sqrt(16)*sqrt(2) = 4*sqrt(2)

The last thing to do is to take the ratio of the hypotenuse over the opposite side. Recall that csc, aka cosecant, is the reciprocal of sine.

sin = opposite/hypotenuse

csc = hypotenuse/opposite

---------

So we get the following

[tex]\csc{\theta} = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc{\theta} = \frac{4\sqrt{2}}{\sqrt{7}}\\\\\csc{\theta} = \frac{4\sqrt{2}*\sqrt{7}}{\sqrt{7}*\sqrt{7}}\\\\\csc{\theta} = \frac{4\sqrt{2*7}}{\sqrt{7*7}}\\\\\csc{\theta} = \frac{4\sqrt{14}}{\sqrt{49}}\\\\\csc{\theta} = \frac{4\sqrt{14}}{7}\\\\[/tex]

So that's why the answer is choice A.

Answer:

4 option

Step-by-step explanation:

Answer:

Step-by-step explanation:

4986 ounces/m³

Step-by-step explanation:

1 kilogram = 35.274 ounces

1 cubic foot = 0.0283 cubic metre

We are converting kg/ft³ to ounces/m³

Hence:

4kg/ft³ × 35.274 ounces/ 1 kg × 1 ft³/0.0283m³

= 4985.7243816 ounces/m³

Approximately to the nearest whole number = 4986 ounces/m³

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The density of the material is approximately 123 ounces per cubic meter.

Density [tex](\(D\))[/tex] is defined as mass [tex](\(m\))[/tex] per unit volume [tex](\(V\))[/tex], and it is calculated using the formula:

[tex]\[ D = \frac{m}{V} \][/tex]

In this case, the density is given in kilograms per cubic foot. To convert this to ounces per cubic meter, we need to perform the following steps:

Step 1: Convert kilograms to ounces:

1 kilogram = 35.27396 ounces

Step 2: Convert cubic feet to cubic meters:

1 cubic foot = 0.0283168 cubic meters

Now, let's substitute the given values and perform the conversion:[tex]\[ \text{Density in ounces per cubic meter} = \frac{4 \, \text{kg} \times 35.27396 \, \text{ounces/kg}}{1 \, \text{cubic foot} \times 0.0283168 \, \text{cubic meters/cubic foot}} \][/tex]

Solving this equation gives us the density in ounces per cubic meter:

[tex]\[ \text{Density} \approx 123 \, \text{ounces/m}^3 \][/tex]

Rounded to the nearest whole number, the density of the material is approximately 123 ounces per cubic meter.

In summary, we converted the given density from kilograms per cubic foot to ounces per cubic meter using unit conversions.

This involved converting the mass units and volume units before performing the calculation to obtain the final density value in the desired units.

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Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the triangles CAP and HIT are not given. The general explanation to solve sides of similar triangles is as follows;

[tex]\triangle CAP \sim \triangle HIT[/tex] implies that the following sides are similar:

[tex]CA \to HI[/tex]

[tex]AP \to IT[/tex]

[tex]PC \to TH[/tex]

Take for instance:

[tex]CA = y[/tex]     [tex]HI = b[/tex]

[tex]AP = 20[/tex]    [tex]IT = 38[/tex]

Then the solution is:

[tex]CA : HI = AP : IT[/tex]

Substitute values for CA, HI, AP and IT

[tex]y : b= 20 : 38[/tex]

Express as fraction

[tex]\frac{y }{ b}= \frac{20 }{ 38}[/tex]

Multiply both sides by b

[tex]y= \frac{20 }{ 38}*b[/tex]

Substitute 19 for b

[tex]y= \frac{20 }{ 38}*19[/tex]

[tex]y= \frac{20 }{ 2}[/tex]

[tex]y=10[/tex]

Answer:

make y the subject first

Step-by-step explanation:

y=5/7(x) -27/7

parallel lines have equal gradient m1=m2

y-y1=m(x-x1)

y-(-3)=5/7(x-4))

y=5/7(x) -20/7 -3

final answer

y=5/7(x) -41/7

Answer:

Answer:

-80

Step-by-step explanation:

So basically what we need to do is find the value of x that satisfies the equation.

When I mean satisfy, I basically mean a value of x that makes one side of the equals sign equal to the other side of the equals sign.

So in this case, we need -6 = -6.

To find this lets solve the equaion step by step:

-6=x/8+4

So first off, you always want to get the variable on one side, and the number on the other.

This means you want to subtract the 4 from both sides, leaving x/8:

-6=x/8+4

-4       -4

-10=x/8

Whenever x is not 1x, you have to divide or multiply to get it equal to 1x.

If this is a bit confusing, here is an example:

100=10x

We need 1x, but above is 10x. The reason why we want 1x is because it is the lowest ratio, and most accurate x value.

You can think of it like a 1 dollar bill. Its easier and better to use than per say a 3 dollar bill.

So in the example above you would divide by 10, since 10x/10 would equal 1x.

Remember the rule however, that what you do on one side you must do on the other. This emans you would divide both sides by 10:

100/10 =10x/10

=

10=1x

We have in our equation:

-10=x/8

Our x is lower than 1. It x/8. Whenever we have a value of x greater than 1, we divide, like we did in the example. However here, it is below x. So we multiply.

In this case we multiply by 8, since its x/8:

-10 * 8 = x/8 * 8

=

-80=x

So x is equal to -80.

I hope you understand it better now :D

Answer:

$28

Step-by-step explanation:

original price = $40

discount = 30%

discount amount = 30% of original price

=30/100 * 40

=$1200/100

=$12

sale price = original price - discount amount

=$40 - $12

=$28

Answer:

In other words y = 2-x

Put in some values of x and see which graph matches the given ys.

The last graph

Answer:

b

Step-by-step explanation:

Answer:

$56.32

Step-by-step explanation:

Find the selling price by multiplying the original cost by 1.76:

32(1.76)

= 56.32

So, the selling price is $56.32

Answer:

8x² + 8

Step-by-step explanation:

Given

(x² + 3)² - (x² - 1)² ← expand factors using FOIL

= [tex]x^{4}[/tex] + 6x² + 9 - ([tex]x^{4}[/tex] - 2x² + 1) ← distribute by - 1

= [tex]x^{4}[/tex] + 6x² + 9 - [tex]x^{4}[/tex] + 2x² - 1 ← collect like terms

= 8x² + 8

Answer:

7

Step-by-step explanation:

70+16x-2

68+16x=180

16x=180-112

x=112/16

x=7

Answer:

x = 7

Step-by-step explanation:

70 + 16x - 2 = 180 degree (being co interior angle)

68 + 16x = 180

16x = 180 - 68

16x = 112

x = 112/16

x = 7

Answer:

m∠6 = 116°

Step-by-step explanation:

first find x:

7x - 17 = 2x + 78

subtract 2x from both sides: 5x - 17 = 78

add 17 to both sides: 5x = 95

divide by 5: x = 19

plug x into 7x - 17

7(19) - 17 = 116

∠6 and 7x - 17 are vertical angles and therefore congruent, so m∠6 also = 116°

Answer: 44º

Step-by-step explanation:

Hi there! To start out, disregard Y and Z, as they are just there to trip you up.

Use the Triangle Sum Theorem to find out the question! This theory states that all angles in a triangle add up to 180 degrees. So, just set up an equation, like the one down below!

82+54+X=180

Then, add the whole numbers!

136+X=180

Then isolate X by using inverse operations!

136+X-136=180-136

Then your answer is there!

X=44

If you have any follow up questions, please let me know! Have a nice day

Answer:

If the probability is that it WILL rain 1/5.  Then the remaining chances are the number it will not rain.  The denominator tells us that there are at total of 5 chances.  That leaves a 4/5 chance it will not rain.

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Let's say that the amount of lollipops Lydia buys is represented by x and the number of candy bars is represented by y. For each x, Lydia spends 0.50, and for each y, Lydia spends 1.50. This means that the total amount she spends can be represented by the equation 0.50*x+1.50*y. Our equation is then 0.50*x+1.50*y=15

Using our equation, we can plug 6 in for x, resulting in 0.50*6+1.50*y=15, so [tex]0.50x+1.50y=15\\0.5(6)+1.50y=15\\3+1.50y=15\\1.50y=12\\y=8[/tex]

In this set of equations, we plugged 6 in, multiplied it out, then subtracted 3 from both sides, and finally divided both sides by 1.50 to get 8 as our answer.

Answer:

9. a) 180 - (55+90) = a

b) a=35 degrees

10. a) 2w + 3w + 40 = 180

b) w=28

c) 2w=56      3w=84

Step-by-step explanation:

Answer:

the person above is 100% right trust me :)

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

Given

3(x - 1) - 2(x - 1) = 7 ← distribute both parenthesis on left side

3x - 3 - 2x + 2 = 7 , simplifying

x - 1 = 7 ( add 1 to both sides )

x = 8

Answer:

c < 56

Step-by-step explanation:

Maya buys candy that costs $8 per pound. She will buy less than 7 pounds of candy. What are the possible amounts she will spend on candy? Use c for the amount (in dollars) Maya will spend on candy. Write your answer as an inequality solved for c.

c < 7 × $8

c < $56

Answer:

5940 rupees

Step-by-step explanation:

99 multiplied by 29×5 is 5940

Answer:

[tex]\text{(b) }[/tex] ₹[tex]5,940[/tex]

Step-by-step explanation:

Each pair of scissors on the chart represents 5 haircuts, as indicated by the key. There are 2 scissors on Saturday and 10 scissors on Sunday, hence a total of 12 scissors over the weekend. Therefore, there were [tex]12\cdot 5=60[/tex] haircuts over the weekend.

Since the salon charges 99 rupees per cut, they made a total of [tex]99\cdot 60=\boxed{5,940}[/tex] rupees over the weekend.

Answer:

The unknown side is 140

Step-by-step explanation:

Let the unknown side be x

Using ratios

90         90+36

------ = -----------

x            x+56

90         126

------ = -----------

x            x+56

Using cross products

90(x+56) = 126x

Distribute

90x+5040 = 126x

Subtract 90x

5040 = 36x

Divide by 36

140 =x

Answer:

16 pi

Step-by-step explanation:

The base is the circle

A = pi r^2

A = pi (4)^2

A = 16 pi

Answer: 16[tex]\pi[/tex] square units

Step-by-step explanation:

This figure is a cylinder. The base of a cylinder is a circle. The formula for finding the area of a circle is [tex]\pi r^2[/tex]. The radius in the image is 4. Now we can solve

[tex]\pi 4^2\\\pi 16\\16\pi[/tex]