Alicia is sewing a rectangle bedspread that measures 72 inches by 60 inches. The bedspread is red with a gold circle 18 inches in diameter in the center. To the nearest square inch, what is the area of the bedspread that is red?

Answer:

First choice V = 18,432π m^3; S = 2,304π m^2

Step-by-step explanation:

Start with the two formulas:

Volume of a circle:

[tex] V = \dfrac{4}{3} \pi r^3 [/tex]

Surface area of a circle:

[tex] S = 4 \pi r^2 [/tex]

Now use r = 24 m in each formula.

Volume:

[tex] V = \dfrac{4}{3} \pi (24~m)^3 [/tex]

[tex] V = \dfrac{4}{3} \pi (13,824~m^3) [/tex]

[tex] V = 18,432\pi~m^3 [/tex]

Surface area:

[tex] S = 4 \pi r^2 [/tex]

[tex] S = 4 \pi (24~m)^2 [/tex]

[tex] S = 4 \pi (576~m^2) [/tex]

[tex] S = 2,304\pi ~m^2 [/tex]

Answer: First choice V = 18,432π m^3; S = 2,304π m^2

Correct  Option 2: The volume of the sphere is 972π cm³ and its surface area is 324π cm²

To determine the volume and surface area of a sphere, we use the formulas:

Given the radius (r) of the sphere is 9 centimeters:

Hence, the volume of the sphere is 972π cm³ and the surface area is 324π cm².

Answer: OPTION D

Step-by-step explanation:

You need to remember this property:

[tex]\frac{\sqrt{x} }{\sqrt{y} }=\sqrt{\frac{x}{y} }[/tex]

And remember that:

[tex]\frac{a}{a}=1[/tex]

Then, the first step is rewrite the expression:

[tex]\frac{\sqrt{30(x-1)} }{\sqrt{5(x-1)^2}}[/tex] [tex]=\sqrt{\frac{30(x-1)}{5(x-1)^2}} }[/tex]

Now, to find the corresponding equivalent expression, you need to simplify the expression.

Therefore, the equivalent expression is the following:

[tex]\sqrt{\frac{6}{(x-1)}} }[/tex]

Finally, you can observe that this matches with the option D.

Answer:

Choice D

Step-by-step explanation:

The division of the two radicals can be re-written in the following format;

[tex]\frac{\sqrt{30(x-1)} }{\sqrt{5(x-1)^{2} } }[/tex]

Using the properties of radicals division, the expression can further be written as;

[tex]\sqrt{\frac{30(x-1)}{5(x-1)^{2} } }[/tex]

We simplify the terms under the radical sign to obtain;

[tex]\sqrt{\frac{6}{x-1} }[/tex]

Choice D is thus the correct solution

ANSWER

x coordinates of the intersection points

EXPLANATION

The given system of equations is:

[tex]y = 4 {x}^{2} - 3x + 6[/tex]

[tex]y = 2 {x}^{4} - 9 {x}^{3} + 2x[/tex]

We want to use the graph of these functions to solve

[tex] 4 {x}^{2} - 3x + 6 = 2 {x}^{4} - 9 {x}^{3} + 2x [/tex]

The point of the intersection of the graph gives the solution to the simultaneous equation above.

Hence the x-coordinates of the intersection points gives the solution set of

[tex]4 {x}^{2} - 3x + 6 = 2 {x}^{4} - 9 {x}^{3} + 2x [/tex]

The last choice is correct.

Answer: It's D

Step-by-step explanation:

Answer:

Option c.) the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.

Step-by-step explanation:

step 1

Find the volume of one ball

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=1.5\ in[/tex]

[tex]V=\frac{4}{3}(3.14)(1.5)^{3}=14.13\ in^{3}[/tex]

therefore

The volume of two balls is

[tex](2)*14.13=28.26\ in^{3}[/tex]

step 2

Find the volume of the cylinder

The volume of the cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]r=1.5\ in[/tex]

[tex]h=1.5*4=6\ in[/tex]

substitute

[tex]V=(3.14)(1.5)^{2}(6)=42.39\ in^{3}[/tex]

therefore

The wasted space with the cylinder is equal to

[tex]42.39\ in^{3}-28.26\ in^{3}=14.13\ in^{3}[/tex]

step 3

Find the volume of the square prism

The volume of the square prism is equal to

[tex]V=b^{2}h[/tex]

we have

[tex]b=1.5*2=3\ in[/tex]

[tex]h=1.5*4=6\ in[/tex]

substitute

[tex]V=(3)^{2}(6)=54\ in^{3}[/tex]

therefore

The wasted space with the prism is equal to

[tex]54\ in^{3}-28.26\ in^{3}=25.74\ in^{3}[/tex]

step 4

Find the difference of the wasted space

[tex]25.74\ in^{3}-14.13\ in^{3}=11.61\ in^{3}[/tex]

Answer:

C. the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.

Step-by-step explanation:

if you find the volumes of both shapes and subtract the volumes of the two balls and then subtract the two remaining values you get a difference of 11.6 inches. This makes the cylinder smaller and therefore uses less space.

Answer:

C) y = -cos(x) +2

Step-by-step explanation:

The centerline is 2, so 2 is added. That leaves out choices A and B.

There is a minimum (not a maximum) at x=0, so the multiplier is negative, eliminating choice D.

The correct equation is that of C: y = -cos(x) +2.

The situation that can be modeled by the given inequality is required.

Option D. is correct.

Let [tex]x[/tex] be the number of T shirts bought

The initial amount of money is $50

The savings should be at least $8 so more than or equal to $8.

The required inequality is [tex]50-12x\geq 8[/tex]

The inequalities of the other options that are not correct are

C. [tex]50-12x<8[/tex]

Here, [tex]x[/tex] is number of weeks

B. [tex]50-12x\geq 8[/tex]

Here [tex]x[/tex] is the number of packages bought.

So, [tex]12x[/tex] will be the total number of pretezels[/tex]

A. [tex]50-8x<12[/tex]

Here [tex]x[/tex] is the number of weeks.

So, option D. is correct.

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Answer:

C.

Step-by-step explanation:

Answer:  c) 56 and 88

Step-by-step explanation:

95% is 2 standard deviations above and below the mean.

  72 ± 2(8)

= 72 ± 16

= 56 and 88

Answer:

-35/7

3/-1

Step-by-step explanation:

If you divide a positive number by a positive number

the outcome will be positive

If you divide a positive number by a negative number the outcome will be negative

If you divide a negative number by a negative number the outcome will be positive

If you have any questions do not hesitate to ask

:)

3/-1 is also a solution

Answer:

The equation of this line is therefore    y = 2x + 3.

Step-by-step explanation:

this line passes thru the points (0, 3) and (3, 9).  As we move from  (0, 3) to (3, 9), x increases by 3 and y increases by 6.  Thus, the slope of this line is

m = rise / run = 6/3, or m = 2.  Inserting the known info (m = 2, x = 0, y = 3) into y = mx + b, we get:  3 = 2(0) + b, so we see that b = 3.

The equation of this line is therefore    y = 2x + 3.

Answer:

121

Step-by-step explanation:

First, we find the z-score for 13 cm:

z = (x - μ) / σ

z = (13 - 11.2) / 2.1

z = 0.86

Next, we use a calculator or a z-score table to find P(x<0.857).

P(x<0.86) = 0.8051

So the number of green beans in a bag of 150 less than or equal to 13 cm is:

0.8051 * 150

121

The number of green beans that is 13 centimeters or shorter will be 121. Then the correct option is C.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The z-score is given as,

z = (13 - 11.2) / 2.1

z = 1.8 / 2.1

z = 0.587

The number of green beans that is 13 centimeters or shorter will be given as,

⇒ 150 x P(z ≤ 0.587)

⇒ 150 x 0.8023

⇒ 121

Thus, the correct option is C.

More about the z-score link is given below.

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Answer:

If im correct from the way this is set up, I believe it is C

Step-by-step explanation:

Answer:

Your answer would be A) y=-x+1

Step-by-step explanation:

Looking at each value in the table you can take x, make it a negative, then add 1 for it to equal y. Hope this helped and have a wonderful day!

Answer: Here...

Step-by-step explanation:

Mean: The average of the numbers so add them up then divide by how many numbers you added

Median: The middle number of the numbers in numerical order

Mode: The number that is repeated the most often

Range: The smallest number subtracted from the larger number

Outlier: A data point or observation that is not with the others so basically the odd one out

Hope this helps Brainliest plz

Answer:

The length of the diagonal of the cube = √(3 × 10²) = √300 cm

Step-by-step explanation:

* Lets revise the properties of the cube

- It has six equal faces all of them are squares

- It has 12 vertices

- The diagonal of the cube is the line joining two vertices in opposite

 faces (look to the attached figure)

- To find the length of the diagonal do that:

# Find the diagonal of the base using Pythagoras theorem

∵ The length of the side of the cube is L

∵ The base is a square

∴ The length of the diagonal d = √(L² + L²) = √(2L²)

- Now use the diagonal of the base and a side of a side face to find the

 diagonal of the cube by Pythagoras theorem

∵ d = √(2L²)

∵ The length of the side of the square = L

∴ The length of the diagonal of the cube = √[d² + L²]

∵ d² = [√(2L²)]² = 2L² ⇒ power 2 canceled the square root

∴ The length of the diagonal of the cube = √[2L² + L²] = √(3L²)

* Now lets solve the problem

∵ The length of the side of the square = 10 cm

∴ The length of the diagonal of the cube = √(3 × 10²) = √300 cm

- Note: you can find the length of the diagonal of any cube using

 this rule Diagonal = √(3L²)

Answer:

its c on endeguity

Step-by-step explanation:

Answer:

B) 10.6 cubic inches

Step-by-step explanation:

Vol = (1/3) base area × hight = (1/3)π×1.5²×4.5

Answer:

C

Step-by-step explanation:

Since EF and GH are parallel lines then

∠EGF = ∠GFH = 60° ( Alternate angles )

Answer:

Part 1) 0.669

Part 2) x=23.78 cm

Step-by-step explanation:

Part 1) we have

cos(48°)

Using a calculator

cos(48°)=0.66913

Round to the nearest thousandth

0.66913=0.669

Part 2) we know that

In the right triangle of the figure

The cosine of angle of 18 degrees is equal to divide the adjacent side to the angle of 18 degrees by the hypotenuse of the right triangle

so

cos(18°)=x/25

x=(25)cos(18°)=23.78 cm

Answer:

Use a calculator to find the cos 48° to the nearest thousandth: A. 0.669

Find the value of x in the triangle below to the nearest hundredth.: B. 23.78 cm

Step-by-step explanation:

I just did these questions and these were the answers that were right for me. Hope this helps!

Answer:

-3

Step-by-step explanation:

[tex]f(x) = 3 - x[/tex]

[tex]g(x) = 4x + 1[/tex]

[tex]h(x) = (g \bullet f) (x) = g(f(x)) \\ = 4(3 - x) + 1 \\ = 13 - 4x[/tex]

then

[tex]h(4) = 13 - 4 \times 4 = - 3[/tex]

Answer:

  74°

Step-by-step explanation:

The given congruence relations mean ...

  3x -7 = 6x -88

  81 = 3x . . . . . . . add 88-3x

  (3x -7)° = (81 -7)° = 74°

The measure of angle XMZ is 74°.

Answer:

101.956 cm²

Step-by-step explanation:

The area (A) of a parallelogram is calculated using the formula

A = bh ( b is the base and h the perpendicular height )

here b = 14.2 and h = 7.18, hence

A = 14.2 × 7.18 = 101.956 cm²

If he bought 4 hats for $5 each and he spent a total of $44, he spent $44 - $20 in shirts.

44 - 20 = 24

2 shirts for $24 is 1 for 12

$12 for each shirt

Hope it helps :)

Answer:

1 shirt= $12

Step-by-step explanation

we can make an equation where S= shirts, and H for hats. this would look like 2S+4H=44. now we get the info H=5(dollars). we plug it in to get 2S+4 x 5=44. now we simplify to get 2S+20=44. we subtract 20 from both sides to simplify further to get 2S=24. now we can divide this by 2 on each side to get S=11, and since S is the shirts, it says one shirt is =to 11, or 1 shirt= $12

Answer:

Option D

y = x^2 − 6

y = x − 4

Step-by-step explanation:

we know that

The y-intercept of the quadratic equation is the point (0,-6) (see the graph)

Could be option A or option D

The y-intercept of the linear equation is the point (0,-4) and the x-intercept is the point (4,0)

Could be option D

therefore

The system of equations is the option D

Verify

[tex]y=x^{2}-6[/tex]

[tex]y=x-4[/tex]

using a graphing tool

see the attached figure

The system of equations is the option D

Answer:

5

Step-by-step explanation:

.

.

.

Answer:

A) 2x³+11x²+8x-16

Step-by-step explanation:

When you multiply s(x) by t(x) you get something like this:

[tex]s(x) \times t(x) = (2 {x}^{2} + 3x - 4) \times (x + 4) \\ = 2 {x}^{3} + 3 {x}^{2} - 4x + 8 {x}^{2} + 12x - 16 \\ = 2 {x}^{3} + 11 {x}^{2} + 8x - 16[/tex]

Answer:  A) 2x³ + 11x² + 8x - 16

Step-by-step explanation:

s(x) · t(x) = (x + 4)(2x² + 3x - 4)

             = x(2x² + 3x - 4) + 4(2x² + 3x - 4)

             =   2x³ + 3x² - 4x  + 8x² + 12x - 16

             =   2x³  + (3x² + 8x²) + (- 4x + 12x) - 16

             =  2x³          + 11x²              + 8x      - 16

Answer:

1677

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) p=0.35 and q = 0.65

Std error =[tex]\sqrt{\frac{0.35*0.65}{n} }[/tex]

Margin of error = 2.58*std error = 3%

i.e. [tex]2.58*0.477/\sqrt{n}= 0.03\\n = 1683\\[/tex]

Approximately 1677

2) Same method as above

Margin of error = 1.645 * [tex]\sqrt{\frac{0.85(0.15)}{n} }[/tex]=0.02

Hence n = 863

3) Margin of error = 1.96*[tex]\sqrt{\frac{0.45(0.55)}{875} }[/tex]

=0.0329

=0.033

(option d)

Answer:

I think it is 285 bc 15*19 is 285

The answer is:

The height of the  lightning rod is 27.4 feet.

To solve the problem, we need to use the given information about the two points of observation, since both are related (both finish and start at the same horizontal distance) we need to write to equations in order to establish a relationship.

So, writing the equations we have:

We know that the angle of elevation from the base of the buildings is 36°

Also, we know that from the same location, the angle of elevation to the top of the lightning rod is 38°.

Using the information we have:

To the top of the building:

[tex]tan(\alpha )=\frac{DistanceToTheTopOfTheBuilding}{BuildingBase}\\\\tan(36\°)=\frac{DistanceToTheTopOfTheBuilding}{BuildingBase}[/tex]

To the top of the lightning rod:

[tex]tan(\alpha )=\frac{DistanceToTheTopOfTheLightningRod}{BuildingBase}\\\\tan(38\°)=\frac{DistanceToTheTopOfTheLightningRod}{BuildingBase}[/tex]

Now, isolating we have:

[tex]tan(36\°)=\frac{DistanceToTheTopOfTheBuilding}{BuildingBase}\\\\DistanceToTheTopOfTheBuilding=tan(36\°)*BuildingBase \\\\DistanceToTheTopOfTheBuilding=tan(36\°)*500feet=363.27feet[/tex]

Also, we have that:

[tex]tan(38\°)=\frac{DistanceToTheTopOfTheLightningRod}{BuildingBase}\\\\DistanceToTheTopOfTheLightningRod=tan(38\°)*BuildingBase\\\\DistanceToTheTopOfTheLightningRod=tan(38\°)*500feet=390.64feet[/tex]

Therefore, if we want to calculate the height of the lightning rod, we need to do the following:

Let "x" the distance to the top of the building and "y" the distance to the top of the lightning rod, so:

[tex]LightningRodHeight=y-x=390.64feet-363.27feet=27.37feet[/tex]

Rounding to the nearest foot, we have:

[tex]LightningRodHeight=y-x=390.64feet-363.27feet=27.37feet=27.4feet[/tex]

Hence, the answer is:

The height of the lightning rod is 27.4 feet.

Have a nice day!

To find the height of the lightning rod, create two right triangles using the tangent function and the given angles of elevation. Use the distance from the base to the location as the base of both triangles. Calculate the height of the building and the height of the lightning rod separately using trigonometry.

To find the height of the lightning rod, we can use the concept of trigonometry and create a right triangle with the base of the triangle as the distance from the base of the building to the location, the height of the building as the vertical side of the triangle, and the angle of elevation to the top of the building as one of the acute angles. Using the tangent function, we can calculate the height of the building to be approximately 287 feet. Next, we can create another right triangle with the same base the height of the lightning rod as the vertical side, and the angle of elevation to the top of the lightning rod as one of the acute angles. Again, using the tangent function, we can calculate the height of the lightning rod to be approximately 310 feet. Therefore, the height of the lightning rod is approximately 310 feet.

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Answer: The true statements are:

The "(7 + 2x)" in the first term is a factor.

The "9" in the second term is a coefficient.

The "3y" in the first term is a factor.

Step-by-step explanation:

Answer:

Option 1 and 2.

Step-by-step explanation:

Given : Expression  [tex]3y(7 + 2x) + 9xy - 10[/tex]

To find : Observe the expression below and select the true statement(s)?

Solution :

Using definition mentioned below :

We can say that statements which are true are

1) The "(7 + 2x)" in the first term is a factor.  

2) The "9" in the second term is a coefficient.  

Rest are false.

Therefore, option 1 and 2 is correct.

The Answer will be 3.28 h

hope this will Help:)

Answer:

3.28

Step-by-step explanation:

z score is:

z = (x - μ) / σ

For z = -1.2, μ = 4.6, and σ = 1.1:

-1.2 = (x - 4.6) / 1.1

x = 3.28

Answer:

the final answer is 50/11

Step-by-step explanation:

Here let's regard the first number of this geometric series as 0.54, holding the 4 to include later.  The next is 0.0054, the next 0.000054, and so on.

Thus, the common ratio is 1/100.  Then the sum of the infinite series, not including that 4, is

   a          0.54        0.54

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

 1 - r       1 - 1/100     99/100

                                                                                      54

Multiplying both 0.54 and 99/100 by 100 results in ------- and this

                                                                                        99     0.545454....

Now add the 4 back in, obtaining 4  54/99, or (396 + 54) / 99.

This is the same as 450 / 99.  You can readily check with a calculator to see whether this is equivalent to the given   4.54545454545...

Note that 450/99 is in the form p/q (not pq), where p and q are positive integers.  But also note that 450/99 can be reduced to 150/33, or

50/11.  A calculator will show you that 50/11 is equivalent to the given   4.54545454545...

Hence, the final answer is 50/11 (in the form p/q, NOT pq).

The number 4.54545454545... can be expressed as a rational number in the form of p/q as 50/11.

To express the given number 4.54545454545... as a rational number in the form p/q, we need to use the concept of repeating decimals.

Let x = 4.54545... We can then write 100x = 454.54545... Subtracting the first equation from the second, we get 99x = 450. Solving for x gives us x = 450/99.

This fraction can be simplified further by dividing both the numerator and the denominator by their greatest common divisor. In this case, 450 and 99 share a common factor of 9. Dividing both numbers by 9 gives us 50/11, which is the simplest form of this fraction.

Therefore, 4.54545454545... as a rational number in the form p/q is 50/11.

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Answer:

[tex]\boxed{365}[/tex]

Step-by-step explanation:

Let g = number of girls  

and b = number of boys  

We have conditions (1) and (2):  

[tex]\begin{array}{lrcll}(1) &\frac{2}{7}g & = & \frac{3}{5}b & \\(2) & g - b & = & 165 &\\(3) & 10g & = & 21b & \text{Multiplied each side of (1) by lcm of denominators}\\(4)& g & = & 165 + b &\text{Added b to each side of (2)}\\ & 10(165 + b) & = & 21b & \text{Substituted 4 into (3)} \\\end{array}[/tex]

[tex]\begin{array}{lrcll} & 1650 + 10b & = & 21b & \text{Distributed the 10} \\ & 1650 & = & 11b & \text{Subtracted 10b from each side} \\ (5) & b & = & 150 &\text{Divided each side by 11} \\ & g - 150 & = & 165 & \text{Substituted (5) into (2)} \\ & g & = & 215 &\text{Added 150 to each side} \\\\ & g + b & = & 365 &\text{Added girls and boys} \\\end{array}[/tex]

[tex]\text{The number of children at the festival was \boxed{\textbf{365}}}[/tex]

Check:

[tex]\begin{array}{rlcrl}\frac{2}{7}\times315& = \frac{3}{5} \times150 & \qquad & 315 - 160 & =165\\90 & = 90& \qquad & 165 & = 165\end{array}[/tex]

Answer: 20,000

Step-by-step explanation:

every 30 years 10,000 adds to the population

30 years=10,000 people        

60 years=20,000 people