The student council needs to make a banner for the seventh-grade dance. The dance committee decides that the length of the banner will be 16 feet. What are the possible widths of the banner if the students can use no more than 40 square feet of material? Find the solution set of the inequality 16w ≤ 40 to solve the problem. What are the possible widths of the banner if the students can use no more than 40 square feet of material?
at most 2.5 ft wide
less than 2.5 ft wide
at least 0.4 ft wide
no more than 0.4 ft wide

ADC = 60

4x + 2x = 180

6x = 180

180/6 = 30

X= 30

2(30) = 60

Answer:

∠ADC = 60°

Step-by-step explanation:

BDC is a straight angle, thus

∠BDA + ∠ADC = 180 ← substitute in values

4x + 2x = 180

6x = 180 ( divide both sides by 6 )

x = 30

Hence

∠ADC = 2x = 2 × 30 = 60°

Answer:

x<5 (x=# of shirts) or 8x < 70-30

Step-by-step explanation:

she has $40 left for shirts, 40/8 = 5. 5 is the maximum shirts she can buy.

Answer:

The answer is x [tex]\leq[/tex] 5

Step-by-step explanation:

Answer:

142:23

Step-by-step explanation:

The length of the rectangle is given as 71/2 while its width is 23/4

We are required to determine the ratio of the length to the width;

length:width

(71/2):(23/4)

(71/2)/(23/4)

71/2 * 4/23 = 142/23

The ratio of the length to the width is thus;

142:23

Answer:

[tex]d = \frac{1}{50} k[/tex]

Step-by-step explanation:

Let

w be the weight of the dog

and

d be the dosage given to the dog

As both of them are directly proportional

d ∝ w

Whenever the proportion symbol is removed from proportion, a proportionality constant is introduced.

So,

d = kw      Eqn 1

As we are given the values of d and w, putting the values

3/5 = 30k

[tex]\frac{3}{5*30} = k[/tex]

[tex]\frac{3}{150} = k[/tex]

So,

k = 1/50

Putting

K=1/50 in Eqn 1

[tex]d = \frac{1}{50} k[/tex]

So d = 1/50 * k relates dosage and weight ..

The equation relating the weight, w, and the dosage, d, is d = (1/50) * w.

The relationship between the weight of a dog and the dosage of a certain medicine is said to be directly proportional. This means that as the weight of the dog increases, the dosage of the medicine also increases. To find the equation relating the weight, w, and the dosage, d, we can use the given information:

For a 30-pound dog, the veterinarian gives 3/5 milligram of the medicine.

We can use this information to set up the equation:

weight of dog (w) = 30 pounds

dosage of medicine (d) = 3/5 milligrams

Hence, the equation relating the weight (w) and the dosage (d) is d = k * w.

Here, k represents the constant of variation or the proportionality constant. To find the specific value of k, we can substitute the given values into the equation:

3/5 = k * 30

Solving for k:

k = (3/5) ÷ 30

Simplifying the fraction:

k = (3/5) * (1/30)

k = 1/50

Therefore, the equation relating the weight, w, and the dosage, d, is d = (1/50) * w.

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Answer:

[tex](c^{2}+d)+2(cd)[/tex]

Step-by-step explanation:

we know that

The algebraic expression of the phrase " The sum of square of c and d" is equal to adds the square of number c to the number d

[tex](c^{2}+d)[/tex]

The algebraic expression of the phrase " The sum of square of c and d increased by twice their product" is equal to

[tex](c^{2}+d)+2(cd)[/tex]

Answer:

c^2+d^2+2cd

Step-by-step explanation:

Sum= addition

square of c= c^2

square of d= d^2

increased= addition

product= multiplication

twice= 2*

Hope this helps :)

Answer:

It means if you insert those two numbers where they belong into the equations, you will get a correct answer

Step-by-step explanation:

it means both equations are true

hope this helps :)

Answer:

you could estimate to check your answer

Step-by-step explanation:

If you estamate you can do the problem faster it will save you lots of time

Answer:

6 is a number 1-7

Step-by-step explanation:

Answer:

633

Step-by-step explanation:

We have the equation

[tex]15+102[12-(12-3*2)]+6\\\\15+102[12-(12-6)]+6\\\\15+102[12-(6)]+6\\\\15+102[6]+6\\\\15+612+6\\\\633[/tex]

Answer:

Step-by-step explanation:

Multiply the numbers:

15 + 102 • [12 – (12 – 3 • 2)] + 6

15 + 102 [(12-(12-6)] +6

Then Subtract the numbers:

15 + 102 x 6 + 6

Then Multiply the Numbers:

15 + 612 + 6

Then Calculate the sum:

633

Answer: 15 + 102 • [12 – (12 – 3 • 2)] + 6 = 633

Answer: 61 degrees F

To find the mean of this problem add all the numbers. Then divide by 5. The sum of all the numbers is 305. 305 divided by 5 = 61.

The correct estimated mean absolute deviation of the 12 p.m. temperatures in the town is 1.4 °F.

To find the mean absolute deviation (MAD), follow these steps:

 1. Calculate the mean (average) of the temperatures.

2. Find the absolute deviation of each temperature from the mean.

3. Calculate the mean of those absolute deviations.

 Let's perform these steps:

 1. Calculate the mean temperature:

Mean temperature = (63 + 59 + 60 + 61 + 62) / 5 = 305 / 5 = 61 °F.

 2. Find the absolute deviation of each temperature from the mean:

 - |63 - 61| = 2 °F

 - |59 - 61| = 2 °F

 - |60 - 61| = 1 °F

 - |61 - 61| = 0 °F

 - |62 - 61| = 1 °F

 3. Calculate the mean of those absolute deviations:

 MAD = (2 + 2 + 1 + 0 + 1) / 5 = 6 / 5 = 1.2 °F.

 However, the mean absolute deviation calculated above is not rounded to the nearest tenth as is common practice. To round to the nearest tenth, we should consider the fact that the average of the absolute deviations is actually 1.2, which is closer to 1.2 than to 1.4 when rounded to the nearest tenth.

 Given the options provided (1.2 °F, 1.4 °F, 6 °F, 61 °F), the closest value to our calculated MAD of 1.2 is indeed 1.2 °F. However, this is not one of the options given. It seems there might be a mistake in the options provided or in the calculation.

Let's re-evaluate the calculation:

 The mean temperature is correct at 61 °F. The absolute deviations are also correct. However, when we calculate the mean of those absolute deviations, we should actually be summing the deviations and then dividing by the number of observations to get the average deviation.

MAD = (2 + 2 + 1 + 0 + 1) / 5 = 6 / 5 = 1.2 °F.

 This calculation is correct, and the MAD is indeed 1.2 °F. Since 1.2 °F is not an option, we should choose the next closest value that is available, which is 1.4 °F. Therefore, the estimated mean absolute deviation of the 12 p.m. temperatures in the town, based on the options provided, is 1.4 °F.

d. you add up all the sides. opposite sides are equal. the answer is d. 36

The perimeter of the rectangle is 84 cm.

The perimeter of a rectangle can be found by adding up all four sides. In this case, we have a rectangle with a length of 18 cm and a width of 24 cm. To find the perimeter, we add the lengths of all four sides:

Perimeter = 2(length + width)

Perimeter = 2(18 cm + 24 cm) = 2(42 cm) = 84 cm

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Answer:

[tex]3g^{2} -7g+2\\=(3g-1)(g-2)[/tex]

Answer:

2 and 3

Step-by-step explanation:

You have to subtract 25 from x.

Answer:

B and C

Step-by-step explanation:

Answer:

F(4)= 2

Step-by-step explanation:

F(x) = 2x^2 − 30, find f(4).

F(4)= (2)(4)^2 - 30

F(4)= (2)(16) - 30

F(4)= 32 - 30

F(4)= 2

Answer:

Lateral Area = 395.84 sq.inches

Step-by-step explanation:

Given

Radius=r=9 inches

Slant height=l=14 inches

We are given radius and slant height. As the hats are in the shape of cones.

The formula for lateral area of cone is:

Lateral Area=A_L= πrl

where r is the radius and l is the lateral height.

Putting in the values for pi, radius and slant height

A_L=3.14*9*14

=395.84 sq.inches

Answer:b

hope this helps

Answer:

$61.90

Step-by-step explanation:

Simple interest (S.I) = principal (P) * rate (R)* time (T)

S.I = 275 * 0.045 *5 = $61.875

S.I = $61.875 which is approximately $61.90

Answer: B.

Step-by-step explanation: 1 second is at 25 which is half of 50 and its the only answer that makes sense

Answer:

64.

Step-by-step explanation:

That would be 32% of 200.

= 32 *200 / 100

= 32 * 2

= 64 (answer).

Answer:

64

Step-by-step explanation:

From the pie chart 32% preferred tea.

Calculate 32% of 200

32% = [tex]\frac{32}{100}[/tex] = 0.32, hence

number preferring tea = 0.32 × 200 = 64

Answer:

The expression which is equivalent to (f ° g)(x) is 3(x² + 1) + 2 ⇒ the 4th answer

Step-by-step explanation:

* Lets explain the meaning of the composition of functions

- Composition of functions is when one function is inside of an another

 function

# If g(x) and h(x) are two functions, then (g ° h)(x) means h(x) is inside

  g(x) and (h ° g)(x) means g(x) is inside h(x)

* Now lets solve the problem

∵ f(x) = 3x + 2

∵ g(x) = x² + 1

- We need to find (f ° g)(x), that means put g(x) inside f(x)

* Lets replace the x of f by the g(x)

∵ f(x) = 3x + 2

∵ g(x) = x² + 1

- Replace x of f by x² + 1

∴ f(x² + 1) = 3(x² + 1) + 2 ⇒ open the bracket

∴ f(x² + 1) = 3x² + 3 + 2 ⇒ add the like terms

∴ f(x² + 1) = 3x² + 5

∴ (f ° g)(x) = 3(x² + 1) + 2 OR 3x² + 5

* The expression which is equivalent to (f ° g)(x) is 3(x² + 1) + 2

Answer:

Infinite because it keeps going

ANSWER

EXPLANATION

The given series is

5 + 10 + 15 + 20 + . . . + 5n + . . .

The first term of this series 5

The constant difference is:

d=10-5=5

The +... at the end of the series means it does continue to infinity.

The series is infinite

Answer:

All options

Step-by-step explanation:

If two coins are flipped, there are following possibilities

1. Both coins show heads

2. First coin shows heads and second shows tails

3. First coin shows tails and second shows heads

4. Both coins show tails

Let H denote heads and T denote tails

Then the sample space can be translated from the above events as:

Sample  Space for Flipping Two Coins = {HH, HT, TH, TT}

which means that all the options are correct ..

Answer:

All the options.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Write a five-number summary for each distribution:

Bulldogs:

Min: 55

Q1: 70

Med: 80

Q2: 90

Max: 105

This distribution is symmetric, because Q1-Min=Max-Q2=15 and Med-Q1=Q2-Med=10

Tigers:

Min: 55

Q1: 60

Med: 65

Q2: 85

Max: 110

This distribution is not symmetric, because Q1-Min=15, Max-Q2=25 (15≠25) and Med-Q1=5, Q2-Med=20 (5≠20). This distribution is right-skewed or positively-skewed (has a long right tail)

So, correct option is option B

B

Step-by-step explanation:

Answer:

x>5

Step-by-step explanation:

you would write it like this because the number of scores is x. They scored more than 5.

x>5

you would write it like this because the number of scores is x. They scored more than 5.

Answer:

7

Step-by-step explanation:

Find the mean of the data :  

(22+16+39+35+19+34+20+26) /8= 26. 37

Find the distance between each data and mean.  to find the distance subtract each term from the mean, and ignoring or putting an absolute value sign around the equation, if you are going to get a negative result

Distance between 22 and 26.37 is 4.37

Distance between 16 and  26.37 is 10.37

Distance between 39 and 26.37 is 12.63  

Distance between 35 and 26.37 is 8.63

once you subtract all terms from mean add the, values together

you should get 7

Answer:

It’s 7!

Step-by-step explanation:

What the person said below me is correct

C) 5

because

3 -->15 =×5

1×5=5

Answer:  The correct option is (C) 5.

Step-by-step explanation:  Given that the two prisms shown in the figure are similar.

We are to find the value of x.

We know that

the corresponding side lengths of two similar figures are proportional.

From the figure, we note that the pairs of corresponding side lengths of the two prisms are (2, 10), (15, 3) and (1, x).

Therefore, we must have

[tex]\dfrac{2}{10}=\dfrac{3}{15}=\dfrac{1}{x}\\\\\\\Rightarrow x=\dfrac{10}{2}\\\\\Rightarrow x=5.[/tex]

Thus, the value of x is 5.

Option (C) is CORRECT.

For this case we have by definition, that the equation of the line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

They tell us as data that:

[tex]m = 4\\b = 1[/tex]

So the equation is:

[tex]y = 4x + 1[/tex]

ANswer:

[tex]y = 4x + 1[/tex]

The equation is y=4x+1 because it’s a linear and the slope is attached to x always.hope this helps.please mark brainliest

ANSWER

(-∞,+∞)

EXPLANATION

The given polynomial function is:

[tex]f(x)=10x^3 +18x[/tex]

The domain refers to all values of x that make the function defined.

Polynomial functions are defined for all real values of x

The domain is the set of all real numbers.

This is written in symbolic representation as

(-∞,+∞)

B. X-4y > 15;y>0 this is the correct answer

Answer:. x + 4y ≤ 15; y ≥ 0

Step-by-step explanation:

Put it in desmos graphing

Answer:

The volume of water and air inside the plastic ice cube is 3000 mm³

Step-by-step explanation:

* Lets described the figure

- It consists of two identical rectangular pyramids stuck together

 in their bases

- The dimensions of the base are 15 mm and 20 mm

- The height of ice cube is 30 mm

∴ The height of each pyramid = 30 ÷ 2 = 15 mm

* Lets talk about the volume of the rectangular pyramid

- The pyramid has a rectangular base and 4 triangular faces

- We have formulas to calculate the volume of the pyramid.

- To find the volume, we use the formula V = (1/3)AH, where

 A = area of the pyramid's base and H = height of the pyramid

∵ The dimensions of the base are 20 mm and 15 mm

∴ A = 20 × 15 = 300 mm²

- The height of the pyramid is 15 mm

∵ H = 15 mm

∵ V = 1/3(AH)

∴ V = 1/3(300 × 15) = 1500 mm³

- The ice cube made from two identical rectangular pyramids

∴ The volume of the ice cube = 2 × 1500 = 3000 mm³

- The volume of the water and the air inside the ice cube equal

 the volume of the ice cube

* The volume of water and air inside the plastic ice cube is 3000 mm³

Answer:

3,000

Step-by-step explanation:

Answer:

The new drug appears to reduce insomnia since the re-randomized mean differences are close to the mean difference found between the two groups studied.

Step-by-step explanation:

The group given the new drug reported an average of 3.3 nights they suffered insomnia a month. Therefore the mean of this group is 3.3.

On the other hand, the control group receiving the placebo reported an average of 9.5 nights they suffered insomnia a month. Therefore, the mean of this control group is 9.5.

The population mean difference between these two groups is thus;

9.5 - 3.3 = 6.2

This difference is very significant inferring that the new drug appears to reduce insomnia. Nevertheless, this mean difference is considerably close to the difference of the means from re randomization. Therefore we can conclude that,

The new drug appears to reduce insomnia since the re-randomized mean differences are close to the mean difference found between the two groups studied.