a running relay team ran a 400 meter race in a record-setting time of 36 seconds.what was their average speed to the nearest tenth of a meter per second?

Answer:

The smallest number is two 2

Answer: [tex]45^{\circ}[/tex]

Step-by-step explanation:

[tex]\angle ABC[/tex] is formed by [tex]\overline{AB}[/tex] and [tex]\overline{BC}[/tex], so we can begin by finding their slopes.

[tex]m_{\overline{AB}}=\frac{2-5}{4-7}=-1\\m_{\overline{BC}}=\frac{2-2}{9-4}=0[/tex]

This means that:

[tex]\tan \left(\angle ABC \right)=\left| \frac{-1-0}{1-(0)(-1)} \right|\\\tan \left(\angle ABC \right)=1[/tex]

As [tex]\angle ABC[/tex] is acute, this means [tex]m\angle ABC=\boxed{45^{\circ}}[/tex]

Answer:

5

Step-by-step explanation:

You just multiply the indices by the power so 1/6 x 6 = 1 and 5 to the power of 1 is just 5.

Answer:

Step-by-step explanation:

Remark

This is a proportion question. A proportion is 2 equal ratios that requires you to solve the 4th part when you know the other 3.

Givens

1 foot scale model length

5 feet of actual length

x = length of model

65 feet of actual length

Formula

1 foot / 5 feet = x / 65 feet

Solution

1/5 = x / 65                          Cross multiply

5x = 65                                Divide by 5

5x/5 = 65/5

x = 13

Answer

The model is 13 feet long

Answer:The sum of the interior angles in any triangle must be equal to 180 degrees

In this problem we have a triangle with a 45 degree angle and a 65 degree angle

so

The measure of the third side must be equal to

The triangle is a 45°-65°-70°

Remember that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

In this problem

I can have as many triangles whose internal angles are congruent and their sides are proportional

therefore

More than one triangle can be drawn with these conditions

Step-by-step explanation:

The equation of the line is 5y = 6x + 8 which passes through point C and perpendicular AB.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have a triangle ABC is defined by the points A(2,9), B(8,4), and C(-3,-2).

The slope of the segment AB:

[tex]\rm m =\dfrac{4-9}{8-2}[/tex]

m = -5/6

The slope of the line perpendicular to AB:

Let M is the slope of the line:

mM = -1

(-5/6)M = -1

M = 6/5

The line:

y = Mx + c

y = (6/5)x + c

The line passing through the point C(-3, -2)

-2 = (6/5)(-3) + c

c = 8/5

y = (6/5)x + 8/5

5y = 6x + 8

Thus, the equation of the line is 5y = 6x + 8 which passes through point C and perpendicular AB.

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Answer:

Simple Interest = PTR/100

P=450

T=2

R=3%

Simple Interest = PTR/100

=450×2×3\100

=27

Hence the interest is 27.

Answer: 36 m, 144 m

Step-by-Step Explanation:

a = 14 m

b = 12 m

c = 10 m

Perimeter = a + b + c

Therefore,

= a + b + c

= 14 + 12 + 10

= 26 + 10

=> 36

Perimeter = 36 m

Length of Fence required for Fencing 4 times = Perimeter * 4

Therefore,

= Perimeter * 4

= 36 * 4

= 144

Length of Fence required for Fencing 4 times = 144 m

Answer:

The second step is to isolate the variable by multiplication or division

Step-by-step explanation:

so it should be solving the x

Answer:]

A two-step equation is an algebraic equation that takes you two steps to solve. You've solved the equation when you get the variable by itself, with no numbers in front of it, on one side of the equal sign.

:]   Correct me if i'm wrong  :]

The probability that the dart lands inside the square but not on the circular dartboard is 22% option first is correct.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

A dartboard consists of a circle inscribed in a square.

The area of the square is 64 square inches.

We know the area of the square:

A = a²

a is the side of the square.

64 = a²

a = 8 inches

As the circle inscribed in a square.

The diameter will be 8 inches

The radius of the circle r = 8/2 = 4 inches

Area of the circle = πr² = π(4)² = 16×3.14 = 50.24 inches

P(dart will land on circular dartboard) = 50.24/64 = 0.785

P(dart will not land on circular dartboard) = 1 - 0.785 = 0.215

or

P(dart will not land on circular dartboard) = 21.5% ≈ 22%

Thus, the probability that the dart lands inside the square but not on the circular dartboard is 22% option first is correct.

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Answer:

22%

Step-by-step explanation

Edge.2023!

The missing areas and dimensions of the given squares, rectangles, and triangles are:

2. 36 cm²

3. 21 cm²

4. 9 cm²

5. 5 cm

6. 10 cm

7. 4 cm

8. 8 cm

9. 7 cm

10. 7

11. 10

Area of a square = s²

Area of a rectangle = (length)(breadth)

Area of a triangle = 1/2(base)(height).

2. Area of square = s² = 6² = 36 cm².

3. Area of a rectangle = (length)(breadth) = (3)(7) = 21 cm².

4. Area of a triangle = 1/2(base)(height) = 1/2(3)(6) = 9 cm².

5. Area of a rectangle = (length)(breadth)

60 = (12)(breadth)

Breadth = 60/12

Breadth = 5 cm.

6. Area of a triangle = 1/2(base)(height)

35 = 1/2(7)(height)

Height = (35)(2)/7

Height = 10 cm

7. Area of a square = s²

16 = s²

s = √16

s = length = 4 cm

8. Area of a triangle = 1/2(base)(height)

40 = 1/2(10)(height)

Height = 40/5

Height = 8 cm.

9. Area of a square = s²

49 = s²

s = √49

s = length = 7 cm

10. Area of a rectangle = (length)(breadth)

84 = (12)(breadth)

Breadth = 84/12

Breadth = 7 cm.

11. Area of a triangle = 1/2(base)(height)

35 = 1/2(7)(height)

Height = 70/7

Height = 10 cm.

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Answer:

36 cm

Step-by-step explanation:

See attached image

A cylinder is a three-dimensional structure formed by two parallel circular bases. The lateral and the total surface area of the cylinder are 113.1 yd² and 169.7 yd².

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.

Lateral area of the cylinder = Area of the curved surface

                                             = 2πR × H

                                             = 2 × π × 3yd × 6yd

                                             = 36π yd²

                                             = 113.0973 yd² ≈ 113.1 yd²

The total surface area of the cylinder

         = Area of the two bases + Area of the curved surface

         = 2(π × 3²) + 113.0973 yd²

         = 56.54866 yd² + 113.0973 yd²

         = 169.6459 yd² ≈ 169.7yd²

Hence, the lateral and the total surface area of the cylinder are 113.1 yd² and 169.7 yd².

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So, when we evaluate 1/2 × (6 × 4) ÷ 3 + 2 = 8

To answer the question, we must use the rules of arithmetic in mathematical operations

Mathematical operations are operation which include

In arithmetic, we follow the rule PEMDAS where

So, to evaluate 1/2 × (6 × 4) ÷ 3 + 2, we follow this rule.

So, 1/2 × (6 × 4) ÷ 3 + 2 = 1/2 × 24 ÷ 3 + 2

= 12 ÷ 3 + 2

= 6 + 2

= 8

So,  1/2 × (6 × 4) ÷ 3 + 2 = 8

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The situations that are both statistically fair and morally fair are Situation 2, Situation 3 and Situation 5

For a situation to be fair, the probability of every outcome must be equal.

We can now analyze each option using the above highlight

Situation 1

The probabilities of vowels and consonant are not equal.

Hence, this situation is not fair

Situation 2

People = 4

P(Each) = 1/4

The probability of each participant is equal in the above scenario i.e. 1/4

Hence, this situation is fair

Situation 3

The probability of each cousin is equal in the above scenario i.e. 1/5

Hence, this situation is fair

Situation 4

The probabilities of prime and composite numbers are not equal.

Hence, this situation is not fair

Situation 5

All probabilities are equal in the above scenario i.e. 1/5

Hence, this situation is fair

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The middle term of the expansion of (√x + √y)⁸ is; B: 70 * x² * y²

We want to expand the expression;

(√x + √y)⁸

Now, according to binomial expansion, we know that;

(x + y)ⁿ = ⁿC₀ xⁿ y⁰ + ⁿC₁ xⁿ ⁻ ¹ y¹ + ⁿC₂ xⁿ ⁻ ² y² + ..... + ⁿCₙ x⁰ yⁿ.

Now, for an 8 power binomial, the coefficient of each term from formula are respectively;

1      8      28      56      70     56     28    8      1

The mid term is the fifth term and so, we have;

(⁸C₄ * (√x)⁽⁸ ⁻ ⁴⁾ * (√y)⁴)

⇒ 70 * x² * y²

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Answer:

tickets: $14

popcorn: $10

total: $24

Step-by-step explanation:

2 movie tickets at $7 each is 2*7 which is $14

2 buckets of popcorn at $5 each is 2*5 which is $10

adding these together we get a total spending of $24

Answer:

D*1.2        (OR)      1.2D

Step-by-step explanation:

Because the new menu has one hundred percent of the original menu (D), plus twenty percent, the new menu is 120%, or 1.2

You can then multiply the number of items on the original menu (D), by the new menu's value, which is 1.2 (or 120%).

This brings you to the answer of 1.2D

The perpetual inventory system is an inventory management method that records when stock is sold or received in real-time.

a. Debit Accounts Receivable 12000

Credit  Sales  12000

Debit Cost of Merchandise Sold 6500

Credit    Merchandise Inventory  6500

b. Debit Cash 9500

Credit Sales  9500

Debit Cost of Merchandise Sold 5300

Credit Merchandise Inventory  5300

c. Debit Cash 2900

Credit  Sales  2900

Debit Cost of Merchandise Sold 1700

Credit  Merchandise Inventory  1700

d. Debit Credit Card Expense 385

Credit  Cash  385

e. Debit Credit Card Expense 75

Credit Cash  75

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Using the uniform distribution, considering that the novel has 435 pages, the probability that the page is numbered something between 21 and 31 is:

[tex]p = \frac{10}{435}[/tex]

It is a distribution with two bounds, a and b, in which each outcome is equally as likely.

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

Researching the problem on the internet, it is found that the novel has 435 pages, hence a = 0, b = 435, and the probability that the page is numbered something between 21 and 31 is given by:

[tex]P(21 \leq X \leq 31) = \frac{31 - 21}{435 - 0} = \frac{10}{435}[/tex]

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Answer:

MMm mmm mmm mmm sh get wicked mmm mmm mm like what u saying mmm mmm mmm gla mmmm

Step-by-step explanation:

inflation means, the same item costs more however is the same item, so if a tomato in January 1st costs $1 and by December 31st it costs $2, the price went up by twice, however is same tomato, it didn't become twice as large, anyhow, inflation eats away value and thus is a Decay case.

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &100\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=\textit{elapsed time}\dotfill &15\\ \end{cases} \\\\\\ A=100(1 - 0.04)^{15}\implies A=100(0.96)^{15}\implies A\approx 54.21[/tex]

now, we can look at this value reduction as value that was eaten away from the original.

we can also see the inflationary effect as the new value of the tomato in money terms, that means the tomato went up in price, exponentially by 4% per year, so we can see that as a Growth case in terms of money spent on it.

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &100\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=\textit{elapsed time}\dotfill &15\\ \end{cases} \\\\\\ A = 100(1 + 0.04)^{15} \implies A \approx 180.09[/tex]

now, this is how much the tomato will be priced in money terms in 15 years.

Answer: 30

Step-by-step explanation:

If we were to draw diagonal BD, then we would create two congruent triangles, and we could find the area of each using the formula [tex]A=\frac{1}{2} ab \sin C[/tex].

However, since there are two triangles, we can double this, giving us [tex]A=ab \sin C[/tex].

So, the area is [tex]A=(10)(6)(\sin 30^{\circ})=\boxed{30}[/tex]

answer: 195cm

the photo should explain

Answer:

See Below

Step-by-step explanation:

35% off means you pay 65%

  sooo   A)   .65 x = 136.50   where x = original price

              B)         x = 136.50/.65 = $210 original price

The difference is "You have to pay interest on credit cards but not on charge cards" , Option B

The cards is a financial tool generally issued by banks which let you to borrow money for expenses and make payments afterward in installments.

Credit cards and charge cards differ in two important ways. One is the method of payment

The other difference is

You have to pay interest on credit cards but not on charge cards, as in credit card the person gets lot of time for the payment and the payment can be made in installments and so for this facility extra charge in terms of interest.

Therefore Option b is the correct answer.

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