What is the common difference in the arithmetic sequence 10, 8, 6, 4, ...?

20pts

Answer:

Toby wants to find the volume of a solid toy soldier.He fills a rectangular container 8 cm long, 6 cm wide,and 10 cm high with water to a depth of 4 cm. Toby totally submerges the toy soldier in the water. The height of the water with the submerged toy soldier is 6.6 cm. Which of the following is closest to the volume, in cubic centimeters, of the toy soldier?

A. 125 B. 156 C. 192 D. 208 E.317

The volume of the toy is 125 cubic cm ,option A is the closest answer.

Step-by-step explanation:

Given:

A rectangular container .

Length of the container =8 cm

Width of the container = 6 cm  

Height of the container when water is filled = [tex](h_1)[/tex] = 4 cm

Height of the container when the toy is submerged = [tex](h_2)[/tex] =6.6 cm

Volume of the toy =  Volume of the container with the toy - Volume of the container (with water)

Volume of the toy = [tex](l\times b\times h_2) - (l\times b\times h_1)[/tex]

                              = [tex](l\times b\times)(h_2-h1)[/tex]

                              = [tex](6\times 8)(6.6-4)[/tex]

                              = [tex]48\times 2.6[/tex]

                              = [tex]124.8[/tex] cubic centimeters.

So,the closest value to the volume of the toy is 125 cubic centimeters.

The closest volume, in cubic centimeters, of the toy soldier is 124.8 cm³.

To find the volume of the toy soldier submerged in water, we can use the following steps:

1. Calculate the initial volume of water in the container: 8 cm x 6 cm x 4 cm = 192 cubic cm.
2. Determine the final volume of water with the toy soldier submerged: 8 cm x 6 cm x 6.6 cm = 316.8 cubic cm.
3. Subtract the initial volume of water from the final volume with the toy soldier submerged: 316.8 cubic cm - 192 cubic cm = 124.8 cubic cm.

Therefore, the closest volume, in cubic centimeters, of the toy soldier is 124.8 cm³.

Answer:

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

Step-by-step explanation:

The line is shown in the attachment.

The slope of this line is given by: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

The line passes through (0,1) and (1,5)

Plug in the points to get:

[tex]m=\frac{5-1}{1-0}=4[/tex]

The equation of this line is given by [tex]y=mx +b[/tex], where b=1 is the y-intercept.

From the graph the y-intercept is 1, because the line intersects the y-axis at (0,1).

Therefore the equation is [tex]y=4x+1[/tex]

Answer: answer is 5

Step-by-step explanation:see attachment

First, distinguish the mathematical elements in the expression 12r²4. Multiply the numbers 12 and 4 to give 48, then substitute this value back in to obtain the simplified expression, 48r². The property of multiplication allows this reordering and regrouping without affecting the result.

To simplify the given expression, 12r²4, the first step involves distinguishing the mathematical elements present. In this case, we have multiplication of numbers and a variable. Technically, the expression is equivalent to 12*r^2*4, since there is multiplication between each element.

We proceed with multiplication, starting with the numerical value. In this case, multiply 12 and 4 to get 48. Substitute this resulting value into the expression, yielding 48r². The justification for this operation is the property of multiplication, which is associative and commutative. It allows us to change the order of the numbers being multiplied or group them differently without changing the result.

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Answer:

78.79°

Step-by-step explanation:

A fireman placed a ladder of length 36 feet against a building.

Now, if he placed the ladder 7 feet from the base of the building, then the angle formed between the ladder and the ground will be [tex]\theta[/tex] (Say).

Now, the ladder, the base ground and the building forms a right triangle and the ladder is the hypotenuse of the triangle and [tex]\theta[/tex] is the base angle.

So, [tex]\cos\theta = \frac{\textrm {Base length}}{\textrm {Ladder length}} = \frac{7}{36}[/tex]

⇒ [tex]\theta = \cos^{-1}(\frac{7}{36}) = 78.79^{\circ}[/tex] (Answer)

Answer:

[tex]$ \textbf{P} \textbf{(Sophomore}\hspace{1mm} | \hspace{1mm} \textbf{Boy)} \hspace{1mm}\textbf{=} \hspace{1mm} \frac{\textbf{5}}{\textbf{12}} $ $[/tex]

Step-by-step explanation:

We are asked to find the probability of picking a Sophomore who is a boy.

There are 5 Sophomores who are boys out of total boys.

[tex]$ \textbf{P(A} | \textbf{B)} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{P(A and B)}}{\textbf{P(B)}} $[/tex]

[tex]$ \implies P(Sophomore | Boy) = \frac{P(Sophomore \& Boy)}{P(Boys)} $[/tex]

[tex]$ = \frac{5}{12} $[/tex]

Hence, the answer.

Answer:

The answer is 5 over 12

Step-by-step explanation:

5/12 Fill in 5 then 12

Answer:

See attachment

Step-by-step explanation:

The given system is :

[tex]y = - x + 5[/tex]

[tex]y = \frac{1}{4}x + 10[/tex]

Let us equate both equations and solve for x.

[tex] - x + 5 = \frac{1}{4}x + 10[/tex]

[tex] - 4x + 20 = x + 40[/tex]

[tex]20 - 40 =x + 4x[/tex]

[tex] - 20 = 5x[/tex]

[tex]x = - 4[/tex]

[tex]y = - - 4 + 5 = 9[/tex]

The the two lines of this system will meet at (-4,9)

The graph is shown in the attachment.

There is only one unique triangle that can be drawn with a 35° angle and a 45° angle, as the third angle is determined to be 100° to make the sum 180°.

To determine how many different triangles can be constructed with a 35° angle and a 45° angle, we can use the fact that the sum of angles in a triangle is always 180°. Adding the given angles, we get 35° + 45° = 80°. Subtracting this from 180° gives us the third angle, which is 180° - 80° = 100°. Since the sum of the angles is 180° and all angles are determined, there is only one unique triangle that can be drawn with these angle measures

Answer:

Explanation:

Three or more points are collinear if and only if they are on the same line, and, thus they are solutions, of the same equation of the line.

When you know two points through their coordinates you can always find the equation of the line:

You can find the slope, m, of that line by using the slope formula:

And then, you apply the point-slope equation:

Since you know m, x₁, and y₁, your equation is determined.

Once you have your equation, substitute the x and y coordinates with the coordinates of the point C. If, and only if, the equation is satisfied, the point C is on the same line and the three points are collinear.

Answer:

D

Step-by-step explanation:

The number chart is when the number line helps with the concept of sequencing, and base-10 blocks reinforce place value

In the hundred chart , it consists of the numbers to 100 in sequential order, with ten numbers per row across ten rows.

What is a Number chart and Hundred chart?

Hundred Chart : A hundreds chart is highly useful for children who are learning to count to 100 and strengthening their numerical fluency. With a hundreds chart, numbers read from left to right in rows of 10, starting from the top left corner with the number 1, all the way down to 100 in the bottom right corner

Number Chart : A table listing numbers in numerical order is known as a numbers chart. The numbers in this arrangement will be 1 through 10 in the first line, 11 through 20 in the second line, 21 through 30 in the third line, and so on. There are various types of specific number charts, such as charts for the hundreds that include the digits 1 through 100.

Given data ,

In the hundred chart , it consists of the numbers to 100 in sequential order, with ten numbers per row across ten rows. The layout allows children to count left to right by ones, and down by tens.

And ,

The number chart is when the number line helps with the concept of sequencing, and base-10 blocks reinforce place value

Types of Number Chart

Even Numbers Chart. An even numbers chart represents all the numbers that are divisible by 2.

Odd Numbers Chart. An odd numbers chart represents all the numbers that are NOT divisible by 2

Prime Numbers Chart

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Answer:

$2.17

Step-by-step explanation:

12 goes into 26 2 times.

with 2 left over

2/12 = 1/6

1/6 of a dollar is

divide 100/6 = 16.67

Answer:

19.2 oz water

Step-by-step explanation:

32 oz times 60%

32

x .6

19.2

The over all percent increase in Bill's stock over the two days is 4%

Step-by-step explanation:

The given is:

We need to find what was the overall percent increase in Bill's stock over the two days

Assume that Bill buys the stock by $x

∵ Bill buys the stock by $x

∵ The stock decreases by 20% on the first day

- Find the 20% of x

∵ 20% × x = [tex]\frac{20}{100}[/tex] × x = 0.2 x

∴ The cost at the end of the 1st day = x - 0.2 x = 0.8 x

∵ The stock increases by 30% of its value at the end of the 1st day

- Find the 30% of 0.8 x

∵ 30% × 0.8 x = [tex]\frac{30}{100}[/tex] × 0.8 x = 0.3 × 0.8 x = 0.24 x

∴ The cost at the end of the 2nd day = 0.8 x + 0.24 x = 1.04 x

To find the percentage of increased find the increasing amount and divide it by the original cost, then multiply the quotient by 100%

∵ The increasing amount = 1.04 x - x = 0.04 x

∵ The percentage of increase = [tex]\frac{0.04x}{x}[/tex] × 100%

∴ The percentage of increase = 0.04 × 100% = 4%

The over all percent increase in Bill's stock over the two days is 4%

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Answer:

0.34

Step-by-step explanation:

34%= 34/100

34/100= 0.34

Answer:  .34

Step-by-step explanation:  34% is equal to 34/100, If you turn that into a decimal its 0.34.

Answer:A

Step-by-step explanation:

Answer:

11:48 AM

Step-by-step explanation:

Answer:

11:48 am

Step-by-step explanation:

not sure if I did this right but 60-12=48. before noon would be am so it would be 11:48 am

sorry if its wrong qwq

Answer:

x=2 and y=−2

Step-by-step explanation:

I will solve your system by substitution.

−8x−8y=0;−8x+2y=−20

Step: Solve−8x−8y=0for x:

−8x−8y+8y=0+8y(Add 8y to both sides)

−8x=8y

−8x

−8

=

8y

−8

(Divide both sides by -8)

x=−y

Step: Substitute−yforxin−8x+2y=−20:

−8x+2y=−20

−8(−y)+2y=−20

10y=−20(Simplify both sides of the equation)

10y

10

=

−20

10

(Divide both sides by 10)

y=−2

Step: Substitute−2foryinx=−y:

x=−y

x=−(−2)

x=2(Simplify both sides of the equation)

Answer:

Option A, %29.2

Step-by-step explanation:

Step 1:  Find the total fixed expenses

150 + 30

180

Step 2:  Find the percentage

180 / 617

0.2917... * 100

%29.17

%29.2

Answer:  Option A, %29.2

Answer:

29.2%

Step-by-step explanation:

The fixed expenses are rent and the emergency fund

150+30 =180

The total income is 617

The percent is fixed expenses/income

180/617

.291734198

Multiply by 100% to change from decimal from to percent

29.1734198%

Rounding to the nearest tenth

29.2%

Answer:

(6,4)

Step-by-step explanation:

Multiply 3 by the two equations and add it up but the x's.

Add the y variables and subtract the others

Divide 3y and 12 which gives you 4

Plug in 4y into any equation

Add 24 and leave the 6x which is your answer

Answer:

10

11

12

13

14

15

prime numbers:11,13,15

Answer:

Step-by-step explanation:

15,14,13,12,11,10

Answer: 17/24

Step-by-step explanation: To write the fraction 34/48 in lowest terms, we divide the numerator and the denominator by the greatest common factor of 34 and 48.

Since the factors of 34 are 1, 2, 17, 34 and the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48, the greatest common factor of 34 and 48 is 2.

So we divide the numerator and the denominator of 34/48 by 2.

34 divided by 2 is 17 and 48 divided by 2 is 24.

So 34/48 written in lowest terms is 17/24.

Answer:

3 5/12 cups

Step-by-step explanation:

6 2/3 - 3 l/4= 80/3 - 39/4=41/12=3 5/12

Answer:

Acceleration = -1.25 m/s²

Step-by-step explanation:

Given data:

initial velocity = 5 m/s

Final velocity = 0 m/s since the car stopped

change in time = 4 seconds

Acceleration = change in velocity/change in time

Acceleration = (Final velocity - Initial velocity)/time

Acceleration = (0-5)/4

Acceleration = -5/4

Acceleration = -1.25 m/s²

The acceleration in negative since the car was reducing speed to stop, it can also called deceleration.

It travels 10 m and then stops.

It refers to the study of motion.

Given

Initial speed (u) = 5m/s

Time (t) = 4 sec

We know the equation of motion

[tex]\rm v = u + at\\v^{2}- u^{2} = 2as[/tex]

As final velocity (v) = 0

Then

[tex]v = u +at \\\\0 = 5 + 4a\\\\a= \dfrac{5}{4}[/tex]

then

[tex]\begin{aligned} \rm v^{2}- u^{2} &= 2as \\0^{2} - 5^{2} &= 2*\dfrac{5}{4} *s\\25 &= \dfrac{5}{2}*s \\s &= 10 m\\\end{aligned}[/tex]

Thus, it travels 10 m and then stops.

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Answer:625

Step-by-step explanation:21/(3+4)x9-2=25 and 25^2 (squared) is 625

Answer:

The percent of change is 20%.

And it is increased by last month.

Step-by-step explanation:

Given:

The ice cream parlor has 30 flavors, but for the last week they have only had 25 flavors.

Now, to find the percent of change.

Flavors ice cream parlor has = 30.

Flavors last week they had = 25.

So, the flavors increased from last week by:

[tex]30-25=5\ flavors.[/tex]

Now, to get the percent of change:

[tex]\frac{5}{25} \times 100[/tex]

[tex]=\frac{500}{25}[/tex]

[tex]=20\%.[/tex]

Thus, the percent of change is 20%.

The flavor is increased by last month.

Therefore, the percent of change is 20%.

And it is increased by last month.

Final answer:

The percent of change is a decrease of 16.67%, calculated by subtracting the new amount of flavors from the original, dividing by the original amount, and multiplying by 100.

Explanation:

To find the percent of change in the number of flavors at the ice cream parlor, we will subtract the original amount of flavors from the new amount, divide that by the original amount, and then multiply by 100. The original amount of flavors was 30, and the new amount is 25. Here is the calculation:

Subtract the new amount from the original amount: 30 - 25 = 5

Divide the change by the original amount: 5 ÷ 30 = 0.1667

Multiply by 100 to get the percent: 0.1667 x 100 = 16.67%

The percent of change is a decrease of 16.67% since the number of flavors went down from 30 to 25.

Answer:

42 times.

Step-by-step explanation:

The number of total alphabet = 26 tiles

The number of vowels = 5

The number of consonant = 26 - 5 = 21

Sofia will randomly select 1 tile from the bag and without replacement select another tile from the bag.

The probability to select consonant at first time = 21/26

Total tiles after the first selection = 26 - 1 = 25

The probability to select vowels at second time = 5/25

The probability to select consonant and vowels = [tex]\frac{21}{26} *\frac{5}{25} =\frac{21}{130}[/tex]

Sofia will draw two tiles from the bag 260 times.

The prediction for the number of times Sofia will select a consonant tile and a vowel tile = [tex]\frac{21}{130} *260=42 \ times[/tex]