The circumference of a circular garden is 131.88 feet. What is the radius of the garden?

Answer:

its ok to be mad just take your time

and try i bet you can do this just put in some thinking time

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

The length of the midsegment is half the length of the base segment, so you have ...

... 2(6x +2) = 2x +84

... 10x = 80 . . . . . . . . . simplify, subtract 2x+4

... x = 8

The length of the midsegment is 6·8+2 = 50.

Hi There!

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Question #1:

A video store is selling previously owned DVDs for 40% off the regular price of $15. What is the sale price of the DVDs?

40% = 0.4

15 * 0.4 = $6 (Discount)

15 - 6 = $9 (Sale Price)

Answer: $9

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Question #2:

Due to the increased rate of its rent, the Neat Novelties Store had to markup the cost of its helium balloons by 7%. The store’s original cost for a bunch of 8 primary-colored helium-filled balloons was $7.00. What was the selling price after markup?

7% = 0.07

7 * 0.07 = $0.49 (Increase)

7 + 0.49 = $7.49 (Price after Increase)

Answer: $7.49

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Question #3:

Cecil Home Builders are offering 10% off the option of finishing a basement on all the new homes they are currently building in the Miller Falls Subdivision. The original cost for the finished basement option is $12,000. What is the cost to the buyer after the discount?

10% = 0.1

12,000 * 0.1 = $1,200 (Discount)

12,000 - 1,200 = $10,800 (Price after Discount)

Answer: $10,800

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Hope This Helps :)

Let the Smaller Number be : S

Let the Larger Number be : L

Given : The Sum of Two Numbers is 52

⇒ S + L = 52 --------------- [1]

Given : The Smaller Number is 16 Less than Larger Number.

It Means if we Add 16 to the Smaller Number, It should be Equal to the Larger Number

⇒ S + 16 = L

⇒ S = L - 16 ------------------ [2]

Substituting Equation [2] in Equation [1], We get :

⇒ L - 16 + L = 52

⇒ 2L = 52 + 16

⇒ 2L = 68

⇒ L = 34

Substituting L = 34 in Equation [2], We get :

⇒ S = 34 - 16

⇒ S = 18

⇒ The Larger Number is 34

⇒ The Smaller Number is 18

The two numbers are 34 and 18; 34 being the larger number and 18 being the smaller number.

This is a common type of problem in algebra called a system of linear equations. We can solve it step by step.

So, the larger number is 34 and the smaller number is 18.

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To find the total you would need to multiply the 31.75 by w to get the total amount of his weekly deposits, then that would get added to the initial amount of 249.45

The equation would be 249.45 + 31.75w

249.45 +31.75w

When w = 0, the amount is 249.45. This eliminates the first two choices.

When w = 1, the amount is 31.75 greater than 249.45. This eliminates the last choice.

The remaining choice is the correct one:

... 249.45 +31.75w

It shows the account balance is initially 249.45 and increases with increasing w at the rate of 31.75 per week.

Answer:

E) 15/64

Step-by-step explanation:

To compare the numbers, it works best to express them all using a common denominator. One possibility is 1600, another is 1,000,000.

9/40 = 360/1600

5/16 = 500/1600

9/32 = 450/1600

0.28 = 448/1600

15/64 = 375/1600

The number we're comparing to is 0.25 = 400/1600, so we want to find the closest number to 400 in the set ...

... {360, 500, 450, 448, 375}.

The magnitude of the differences of these numbers from 400 is ...

... {40, 100, 50, 48, 25}.

Clearly, the last number, 15/64 = 375/1600 has the smallest difference from 0.25.

Hey there!

“Which of the following is closest to[tex]0.25[/tex] and why?”

Options

A. [tex]\frac{9}{40}[/tex]

B. [tex]\frac{5}{16}[/tex]

C.[tex]\frac{9}{32}[/tex]

D. [tex]0.28[/tex]

E. [tex]\frac{15}{64}[/tex]

Process of elimination

Well,

Option A can’t be your answer because, [tex]\frac{9}{40}[/tex]equals [tex]0.225[/tex] in decimal form

Option B  can’t be your answer because [tex]\frac{5}{16}[/tex] equals [tex]0.3125[/tex] in decimal form

Option C can’t be your answer because [tex]\frac{9}{32}[/tex]  equals [tex]0.234375[/tex] in decimal form

Option D. Could be your answer  because it’s a tad bit closer by a tad bit but let’s check for option E

Option E can but can’t be your because[tex]\frac{15}{64}[/tex] equals [tex]0.234375[/tex]

This leaves us with  [tex]\boxed{OptionE. \frac{15}{64} }[/tex] as your result

Good luck on your assignment and enjoy your day

~LoveYourselfFirst:)

Answer:

The measure of angle m+n+p is equivalent to 205° (Fourth option)

Step-by-step explanation:

In a quadrilateral, the sum of the interior angles must be equal to 360°:

S=m+n+p+m<VSW+m<WST=360°

m<VSW=65°

Like SW is an altitude, m<WST=90°

Replacing the known values in the formula above:

m+n+p+65°+90°=360°

Adding like terms:

m+n+p+155°=360°

We want m+n+p, then subtracting 155° both sides of the equation:

m+n+p+155°-155°=360°-155°

m+n+p=205°

Answer:

4th Option is correct.

Step-by-step explanation:

Given: STUV ia a trapezoid that is ST is parallel to UV

          SW is altitude that is m∠ SWV = 90°

          m∠ VSW = 65°

To find: measure of m + n + p

Since, ST is parallel to UV.

⇒ n + p = 180° because Sum of Interior Angle on the same side of traversal is 180°

Now, In ΔSVW

∠SVW + ∠SWV + ∠WSV = 180° (Angle sum property of triangle)

m + 90° + 65° = 180°

m + 155 = 180

m = 180 - 155

m = 25°

Thus,  m + n + p = 25 + 180 = 205°

Therefore, 4th Option is correct.

1 27/28 ≈ 1.964 gallons/hour

You want gallons in the numerator of your unit rate, but that unit is in the denominator of the mileage rate. So, the computation must involve division by 28 mpg. Hours is already in the denominator of 55 mph, so the computation will involve multiplication by that rate.

... (55 mi/h)/(28 mi/gal) = (55 mi/h)·(1 gal/(28 mi)) = 55/28 gal/h

... = 1 27/28 gal/h

Final answer:

To calculate the gas usage per hour, divide the speed of 55 mph by the car's fuel efficiency of 28 mpg, resulting in approximately 1.9643 gallons of gas used per hour.

Explanation:

To determine the amount of gas used every hour by a car that gets 28 miles per gallon (mpg) and is travelling at 55 miles per hour (mph), we can use unit analysis as follows:

Therefore, the car uses about 1.9643 gallons of gasoline per hour when driving at a constant speed of 55 mph.

Answer:

[tex]\frac{a}{6}+3[/tex]

Step-by-step explanation:

We have been given an expression and we are asked to simplify our given expression.

[tex]\frac{3}{2} -\frac{1}{2}a+ \frac{2}{3} a+\frac{3}{2}[/tex]

First of all let us combine like terms.

[tex](\frac{2}{3} -\frac{1}{2})a+(\frac{3}{2}+\frac{3}{2})[/tex]

Now let us have a common denominator for the constant terms of a.

[tex](\frac{2*2}{3*2} -\frac{1*3}{2*3})a+(\frac{3}{2}+\frac{3}{2})[/tex]

[tex](\frac{4}{6} -\frac{3}{6})a+(\frac{3}{2}+\frac{3}{2})[/tex]

Now let us simplify the numerators.

[tex](\frac{4-3}{6})a+(\frac{3+3}{2})[/tex]

[tex](\frac{1}{6})a+(\frac{6}{2})[/tex]

Let us divide 6 by 2.

[tex]\frac{1}{6}a+3[/tex]

[tex]\frac{a}{6}+3[/tex]

Therefore, our expression simplifies to [tex]\frac{a}{6}+3[/tex].

Answer:

√5

Step-by-step explanation:

We suppose the vertices are named clockwise around the top of the cube, then clockwise around the bottom (looking down from above the cube), with vertex E below vertex D. Then line AD is in plane ADEF, and line BM is in plane BCHG.

The distance between the named parallel planes is the distance between the lines. That distance is AB, which is given as √5.

_____

A diagram helps.

Answer:

23.  $ 62.76  to the nearest cent

      $63.00 to the nearest dollar

24.  $ 38.42  to the nearest cent

      $38.00 to the nearest dollar

Step-by-step explanation:

When we round to the nearest cent we round the second number after the decimal.  We look at the third number after the decimal.  If it is 5 or above we round up.

When we round to the nearest dollar, we round the number befroe the decimal. We look at the number after the decimal.  If it is 5 or above we round up.

23.  $62.756  we round the 5 so we look at the 6   6>= 5  so we round up

         $ 62.76  to the nearest cent

    $62.756  we round the 2 so we look at the 7  7>= 5  so we round up

          $63.00 to the nearest dollar

24. $38.415 we round the 1 so we look at the 5   5>= 5  so we round up

         $ 38.42  to the nearest cent

    $38.415  we round the 8 so we look at the 4  4< 5  so we leave alone

          $38.00 to the nearest dollar

[tex]3(x-3)=(3)(x)+(3)(-3)=3x-9\\\\A.\ 3x-6\qquad NOT\\\\B.\ 3x-8-1=3x-9\qquad YES\\\\C.\ x+2x-3=3x-3\qquad NOT\\\\D.\ x-3+x-3+x-3=3x-9\qquad YES[/tex]

Answer:

We should expect the population to reach 71000 in 1993.

Step-by-step explanation:

If the population will double every 54 years and the population in 1974 was 56000 people, then the function that represents this situation is

[tex]y=56000\cdot 2^{\frac{x}{54}},[/tex]

where x is time in years since 1974.

Nota that in 1974, x=0, then y=56000 and after 54 years the population will be [tex]y=56000\cdot 2^{\frac{54}{54}}=56000\cdot 2=112000.[/tex]

Therefore, you have to calculate x, when y=71000:

[tex]71000=56000\cdot 2^{\frac{x}{54}},\\ \\\dfrac{71}{56}=2^{\frac{x}{54}},\\ \\\dfrac{x}{54}=\log_2\dfrac{71}{56},\\ \\x=54\log_2\dfrac{71}{56}\approx 18.49[/tex]

Thus, we should expect the population to reach 71000 in 1993 (after full 19 years).

Answer:

[tex]\frac{7\sqrt{58}}{58}[/tex]

Step-by-step explanation:

[tex]\\\text{Given that a point on the terminal side of }\theta \text{ is }(-3,7)\\\\\text{so the terminal side is in Quadrant II}\\\\\text{In the right triangle OMN, using Pythagorean theorem, we get}\\\\\text{ON}=\sqrt{(MN)^2+(OM)^2}\\\\\Rightarrow ON=\sqrt{(7)^2+(-3)^2}\\\\\Rightarrow ON=\sqrt{49+9}\\\\\Rightarrow ON=\sqrt{58}\\[/tex]

[tex]\\\text{we know that in Quadrant II, sine and cosecant are positive.}\\\text{so using the trigonometric ratios, we get}\\\\\sin \theta=\frac{\text{Opposite }}{\text{Hypotenus}}\\\\\Rightarrow \sin \theta=\frac{7}{\sqrt{58}}\\\\\Rightarrow \sin \theta=\frac{7\sqrt{58}}{58}\\[/tex]

Answer:

Independent events

Step-by-step explanation:

We draw a marble, and then put it back.  It was like it never happened.  Then we draw another marble.  The results of the second draw  do not depend on the results of the first draw, so they are independent.

Answer:

option 3

Step-by-step explanation:

sin45° = 11/BC

=>1/√2 = 11/BC

=>BC = 11√2

For this case we must find the hypotenuse (H) or the BC side of the rectangular triangle shown in the figure.

We have to:

[tex]Tangent (B) = \frac {Cathet \ opposite} {Cathet \ adjacent}\\Tangent (45) = \frac {11} {BA}[/tex]

By clearing BA we have:

[tex]BA = \frac {11} {Tangent (45)}\\BA = \frac {11} {1}\\BA = 11[/tex]

The Pythagorean theorem, which states:

[tex]BC = \sqrt {(CA) ^ 2 + (BA) ^ 2}\\BC = \sqrt {(11) ^ 2 + (11) ^ 2}\\BC = \sqrt {(11) ^ 2 + (11) ^ 2}\\BC = \sqrt {2 * 11 ^ 2}\\BC = 11 \sqrt {2}[/tex]

Answer:

[tex]BC = 11 \sqrt {2}[/tex]

Option C

Answer:

225 people.

Step-by-step explanation:

It is 225 people because if you imagine that those 250 people are all made up of groups of ten, there are 25 groups. One person in each group does not prefer David Bright's and there are 25 groups so there are 25 people in the group of 250 people that do not prefer David Bright's. 250-25=225 people.

1. Area of the original patio: 35 ft^2

The original patio has is a rectangle with length = 7 feet and width = 5 feet. The area of a rectangle is given by the product between length and width:

[tex]A=L \cdot W[/tex]

Therefore, since in this case L=7 and W=5, the area of the original patio is

[tex]A=(7 ft)(5 ft)=35 ft^2[/tex]

2. Area of section A: 7x ft^2

Section A is also a rectangle, with length = 7 feet and width = x. Therefore, the area of this section is equal to:

[tex]A=L\cdot W=(7 feet)(x)=7x[/tex]

3. Area of section B: 5x ft^2

Section B is also a rectangle, with length = x and width = 5 feet. Therefore, the area of this section is equal to:

[tex]A=L\cdot W=(x)(5 feet)=5x[/tex]

4. Area of section C:  [tex]x^2 ft^2[/tex]

Section C is a square, with side equal to x. The area of a square is equal to the square of the length of the side:

[tex]A=L^2[/tex]

therefore, in this case, since L = x, the area of this section is

[tex]A=(x)^2 = x^2[/tex]

5. Total area of the new patio using addition: [tex]x^2 +12x+35[/tex] ft^2

The total area of the new patio is equal to the sum of the four areas calculated in the previous sections:

[tex]A=35 +7x +5x+x^2 = x^2 +12x+35[/tex] ft^2

6. Total area of the new patio using multiplication: [tex]x^2+12x+35[/tex]

The total area of the new patio is equal to the product between the length (7+x) and the width (5+x):

[tex]A=(7+x)(5+x)=35+7x+5x+x^2=x^2+12x+35[/tex] ft^2

7. Yes

As we can see by comparing the area calculated in 5. and the area calculated in 6., the two areas are equal.

8. 80 ft^2

We already have the formula for the area of the new patio:

[tex]A=x^2+12x+35[/tex]

If we substitute x=3, we find the value of the area:

[tex]A=(3)^2+12\cdot 3+35=9+36+35=80[/tex]

38% of the bottles Ella collects are plastic and the remaining 62% are glass. Percentage is calculated by dividing the part by the whole and then multiplying by 100.

Ella has 50 bottles in total, out of which 19 are plastic. To find out what percentage of bottles are plastic, we use the formula:

Percentage = (Part/Whole) * 100

Substitute the given values into the formula we get:

Percentage of plastic bottles = (19/50) * 100 = 38%

For the percentage of glass bottles, we first need to find out how many bottles are glass. As the total number of bottles are 50 and 19 of these are plastic, we subtract 19 from 50 to find the number of glass bottles:

Total glass bottles = 50 - 19 = 31

Now we can find out what percentage of bottles are glass using our formula:

Percentage of glass bottles = (31/50) * 100 = 62%

So, 38% of the bottles Ella collects are plastic and 62% are glass.

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Answer:

A) P(flaw) = 0.2

B) P(No major flaws) = 0.95

Step-by-step explanation:

To find the probability of flaws, we can find the probability of no flaws first by dividing by 100:

P(no flaw) = [tex]\frac{80}{100}[/tex] = 0.8

So then:

P(flaw) = 1 - P(no flaw) = 1 - 0.8 = 0.2

P(flaw) = 0.2

First, we need to find the probability of major flaws:

P(major flaws) = [tex]\frac{5}{100} = 0.05[/tex]

P(Major flaws) = 0.05

So to find the probability of no major flaws:

P(No major flaws) = 1 - P(major flaws) = 1 - 0.05 = 0.95

P(No major flaws) = 0.95

According to known percentages, it can be concluded that the probability a part has a flaw is 20% (0.20), and the probability a part has no major flaws is 95% (0.95).

This question is about probability in Mathematics. Specifically, it's based on the principles of probability distribution. Given that we know the percentages for flawless, minorly flawed, and majorly flawed parts, we can calculate the requested probabilities as follows:

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Answer:

13 weeks

Step-by-step explanation:

65=5w

w=65/5

w=13

Final answer:

It will take Mark 13 weeks to save $65 for the skateboard by saving $5 each week.

Explanation:

Mark wants to buy a skateboard that costs $65. He plans to save $5 per week. To calculate how many weeks it will take him to save $65, we divide the total cost of the skateboard by the amount Mark can save per week.

Here's the calculation:

Total cost of the skateboard: $65

Therefore, it will take Mark 13 weeks to save enough money to buy the skateboard.

The confidence interval for confidence level of [tex]1-\alpha[/tex] is

[tex]\left(\overline x-Z_{\alpha/2}\dfrac\sigma{\sqrt n},\overline x+Z_{\alpha/2}\dfrac\sigma{\sqrt n}\right)[/tex]

where [tex]\overline x[/tex] is the sample mean, [tex]Z_{\alpha/2}[/tex] is the critical value for the given confidence level, [tex]\sigma[/tex] is the standard deviation of the population, and [tex]n[/tex] is the sample size. The margin of error is the [tex]Z_{\alpha/2}\dfrac\sigma{\sqrt n}[/tex] term.

a) For a confidence level of [tex]1-\alpha=0.90[/tex], we have [tex]Z_{\alpha/2}=Z_{0.05}\approx1.64[/tex]. So in order to have a margin of error of at most 25 points, we have

[tex]1.64\dfrac{250}{\sqrt n}=25\implies n\approx268.96[/tex]

so Raina should collect a sample of at least 269 students.

b) A confidence interval with a higher confidence level would more closely approximate and reflect the population, so it stands to reason that Luke should collect a larger sample than Raina to meet his 99% confidence spec.

c) For a confidence level of [tex]1-\alpha=0.99[/tex], we have [tex]Z_{\alpha/2}=Z_{0.005}\approx2.58[/tex]. Then the margin of error would at most satisfy

[tex]2.58\dfrac{250}{\sqrt n}=25\implies n\approx665.64[/tex]

so that Luke should collect a sample of at least 666 students.

To calculate the sample size required for a given margin of error in a confidence interval, you can use the formula: n = (z * σ) / E. For Raina's 90% confidence interval with a margin of error of 25, she should collect a sample size of 17. Luke's sample size for a 99% confidence interval should be larger than Raina's, and he should collect a minimum sample size of 26.

To calculate the sample size required for a given margin of error in a confidence interval, you can use the formula:

n = (z * σ) / E

Where:
n = sample size
z = z-score corresponding to the desired confidence level
σ = standard deviation of the population
E = margin of error

(a) To find the sample size for Raina's 90% confidence interval with a margin of error of 25, we plug the values into the formula:

n = (1.645 * 250) / 25 = 16.45

Since sample sizes must be whole numbers, Raina should collect a sample size of 17.

(b) Luke's 99% confidence interval will require a larger sample size because the z-score for 99% confidence is larger than for 90% confidence. Therefore, without calculating the actual sample size, we can determine that Luke's sample size should be larger than Raina's.

(c) To calculate the minimum required sample size for Luke's 99% confidence interval, we use the same formula and plug in the values:

n = (2.576 * 250) / 25 = 25.76

Rounding up, Luke should collect a minimum sample size of 26.

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The axis of symmetry is x=-3 and the minimum or maximum y value is 5.

The vertex is the extreme point of the quadratic function. The graph is left/right symmetrical about the vertex, so the x-value defines the axis of symmetry. The y-value is the extreme, the maximum or minimum.

_____

Comment on the attachment

The graph shows two quadratic functions (red, blue), each with its vertex at (-3, 5). You can see that the line x=-3 is the axis of symmetry of each of them. You can also see that y=5 is the extreme value of the function (maximum or minimum).

Answer:

Length of the segment QS = 11.76 cm

Step-by-step explanation:

We are given with right angle triangle QRS

Angle S is 80 degree and RS = 2 cm

We need to find out QS

RS is adjacent to angle S, so we use cos formula

[tex]Cos (A) = \frac{adjacent}{hypotenuse}[/tex]

[tex]Cos (S) = \frac{RS}{QS}[/tex]

Plug in the angle and RS

[tex]Cos (80) = \frac{2}{QS}[/tex]

Given cos(80) = 0.17

[tex]0.17= \frac{2}{QS}[/tex]

Multiply by QS on both sides

0.17 * QS = 2

Divide by 0.17 on both sides

QS= 11.76470588

Length of the segment QS = 11.76 cm

Answer:

Step-by-step explanation:

The specified set is fairly limited in size, so we can simply check all the choices and see which works:

For n ∈ {1, 2, 3, 4}

... 4n ∈ {4, 8, 12, 16}

Of these values, only the first three {4, 8 12} are less than 16. (16 is equal to 16, not less than 16.)

The corresponding values of n are {1, 2, 3}.

Answer:

The number is 12

Step-by-step explanation:

4 times a number is 8 more than 40

Write the equation

4n=40+8

4n =48

Divide each side by 4 to isolate n

4n/4 = 48/4

n = 12

Answer:

x = 2

Step-by-step explanation:

[tex]11^{2x}=14641\\11^{2x}=11^4\\2x = 4\\x = 2[/tex]

[tex]\text{Use the Pythagorean theorem:}\\\\AB^2+BC^2=AC^2\\\\AC^2=9^2+12^2\\\\AC^2=81+144\\\\AC^2=225\to AC=\sqrt{225}\\\\AC=15\\\\sine=\dfrac{opposite}{hypotenuse}\\\\\text{We have}\ opposite=12\ \text{and}\ hypotenuse=15.\ \text{Substitute:}\\\\\sin\alpha=\dfrac{12}{15}=\dfrac{12:3}{15:3}=\dfrac{4}{5}[/tex]

Final answer:

In a right triangle with given side lengths and angles, sin α can be calculated using the opposite side and the hypotenuse. The sine function in trigonometry is essential for understanding relationships between angles and sides in triangles. The value of sin α = 3/5.

Explanation:

In this case, we have a right triangle ABC with AB = 9, BC = 12, ∠B = 90°, and ∠A = α.

To find sin α, we use the definition of sine in a right triangle: sin α = opposite/hypotenuse.

Therefore, sin α = opposite/hypotenuse = AB/AC = 9/15 = 3/5.