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Question 1:

Removing the zero from 0.76 leads to .76 which is the same as before. Both lead to [tex]7.6 \times 10^{-1}[/tex] in scientific notation.

Personally I prefer the zero up front to make the decimal point stand out easier. Of course it's just a preference, so its up to you to decide which you prefer.

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Question 2:

Taking the zero out of 10.25 leads to 1.25 which is definitely a different number (and smaller). Therefore, this zero is a significant digit compared to before.

Answer:

(4, 1 )

Step-by-step explanation:

x + 6y = 10 → (1)

x + 5y = 9 → (2)

subtract (2) from (1) term by term to eliminate x

0 + y = 1

y = 1

substitute y = 1 into either of the 2 equations and solve for x

substituting into (1)

x + 6(1) = 10

x + 6 = 10 ( subtract 6 from both sides )

x = 4

solution is (4, 1 )

Answer:

Sample Respond: Let's assume it's equal to 14 cm. Substitute this value to the formula for circumference: C = 2 * π * R = 2 * π * 14 = 87.9646 cm . You can also use it to find the area of a circle: A = π * R² = π * 14² = 615.752 cm² . Finally, you can find the diameter - it is simply double the radius: D = 2 * R = 2 * 14 = 28 cm .

Step-by-step explanation:

I got 100% on the quiz

Answer:

132 cm³

Explanation:

[tex]\sf volume \ of \ cone = \dfrac{1}{3} \pi r^2h[/tex]

put radius: 3 cm, height: 14 cm, π as 22/7

[tex]\sf \rightarrow \dfrac{1}{3} *\dfrac{22}{7} * (3)^2(14)[/tex]

[tex]\sf \rightarrow 132 \ cm^3[/tex]

Answer:

a. 1

b. 1

Step-by-step explanation:

by looking at the graph you can deduce the answer.

The equation for the given graph is g(x) = x²-3, and the value of g(2) will be 5.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The equation for the function is,

g(x) = x²-3

The graph of a quadratic function that has something bowl-shaped. Any equation of the form ax²+bx+c=0  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

(x - h)² = 4a(y - k)

(h, k) is the vertex of the parabola:

a = √[(c-h)² + (d-k²]

(c, d) is the focus of the parabola:

To find the value of g (2) the value of the function is,

g(2) = 2²-3

g(2) =8-3

g(2) =5

Thus, the equation for the given graph is g(x) = x²-3, and the value of g(2) will be 5.

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Premium rates are often referred to as premium per fixed face value. Jade's annual premium for a 10-year policy of $200,000 is $1,202.

When it's given that the annual premium is $p per $y face value, then we can calculate the annual premium for $1 face value and then use it to calculate the annual premium for $x. Therefore using proportions, we can write,

$y face value : $p annual premium

[tex]\text{\$1 face value} : \$\dfrac{P}{y}\ \rm annual\ premium[/tex]

[tex]\text{\$x face value} : \$\dfrac{P\times x}{y}\ \rm annual\ premium[/tex]

In the given case, from the tables, we see that for age 34, and 10-year life insurance for the female gender, there is an annual premium of 6.01 per $1000 face value.

Therefore, we will get the value of p = 6.01, and y = 1000.

As mentioned that Jade wants to buy Life insurance for $200,000, therefore, x = $200,000

Putting it in the above-derived formula, we get:

[tex]\text{\$x face value} : \$\dfrac{P\times x}{y}\ \rm annual\ premium[/tex]

[tex]\text{\$200,000 face value} : \$\dfrac{6.01\times 200,000}{1,000}\ \rm annual\ premium = \$1,202\ \rm annual\ premium[/tex]

Hence, Jade's annual premium for a 10-year policy of $200,000 is $1,202.

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Answer:

b 1,202 on edge 2022

Step-by-step explanation:

Answer:

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. (In grammar school, you probably called the domain the replacement set and the range the solution set.

Answer:

B. -∞ [tex]\leq[/tex] x [tex]\leq[/tex] ∞

Step-by-step explanation:

The domain of a graph is all the x-values it covers. Since this graph does not have any arrows at its end or beginning points, we can assume it goes on forever. Lines that go on forever always have an infinite domain.

Answer:

Step-by-step explanation:

9.23

Answer:

I'll assume the ? is supposed to be t^2

See the answers below.

Step-by-step explanation:

h(t) = -4.91t^2 + 24.5t + 1

a) How high is the ball after 1 second?

h(1) = -4.91*(1)^2 + 24.5*(1) + 1

h(1) = 20.59 meters

b) Find the maximum height of the ball to one decimal place.

We can find the maximum height by graphing or by taking the first derivative and setting it equal to zero (the slope is zero at the top of the curve):

  First Derivative

 h(t) = -4.91*(t)^2 + 24.5*(t) + 1

'h(t) = -9.82*(t) + 24.5

0 = -9.82*(t) + 24.5

9.82t = 24.5

t = 2.49 seconds is the time the ball reaches maximum height.  Use that is the equation to find the height:

h(2.49) = -4.91*(2.49)^2 + 24.5*(2.49) + 1

h(2.49) = 31.6 meters

  Graph

See attached graph.  The maximum height occurs at t = 2.49 seconds and the height is 31.6 meters.

c) When does the ball reach its maximum height?

From the first derivative calculation above, t = 2.49 seconds to reach maximum height.  The graph also shows 2.49 seconds.  Better hurry.

d) When does the ball hit the ground?

The can be determined by either direct calculation of from the graph (attached).

Calculation:  

 h(t) = -4.91t^2 + 24.5t + 1

0 (ground) = -4.91t^2 + 24.5t + 1

4.91t^2 - 24.5t - 1 = 0  Solve with the quadratic equation.  I get t = 5.04 seconds

 Graph:

The graph shows 4.95 seconds.  Both agree when rounded to one decimal point:  5.0 seconds.

Answer:

x < 0.382

Step-by-step explanation:

because we know that 34x is smaller than 13. therefore after division we can find out that x must be smaller than 0.382

Answer:

1572864

Step-by-step explanation:

the nth term of a geoemtric series can be calculated using the following rule : [tex]a_n=a_1(r)^n^-^1[/tex]

where an = nth term, a1 = first term , r = common ratio and n = term position.

here, the first term is 6, the common ratio is 4 and the term position is 10 ( because we want to find the 10th term )

so a1 = 6 , r = 4 and n = 10

using these values we plug them into the rule

recall rule : [tex]a_n=a_1(r)^n^-^1[/tex]

==> plug in a1 = 6 , r = 4 and n - 10

[tex]a_1_0=6(4)^1^0^-^1[/tex]

==> subtract 10 and 1

[tex]a_1_0=6(4)^9[/tex]

==> simplify exponent

[tex]a_1_0=6(262144)[/tex]

==> simplify multiplication

[tex]a_1_0=1572864[/tex]

and we are done!

Note:

the common ration was found by dividing the first term by the next term

Answer:

9/7

Step-by-step explanation:

2+2+1+3+4+6+8+1/10+4+3+4

Hope this helps!!!

Answer:

It can produce about 86 candy.

Step-by-step explanation:

434 divided by 5 = 86 with a remainder of 0.8

x           - inf            - 8              1/5              + inf

x+8                   -     0       +                +

5x-1                  -               -          0     +

result               +      0      -          ║     +

x+8/(5x-1) > 0 if x € ] -inf ; - 8[ U ] 1/5 ; + inf [

=> x < - 8 and x > 1/5

The solution to the inequality (x + 8)/(5x - 1) ≤ 0 is:

x ∈ (-∞, -8] ∪ [1/5, ∞)

We have,

To solve the inequality (x + 8)/(5x - 1) ≤ 0,

We can use the following steps:

Step 1:

Find the critical values of x where the expression (x + 8)/(5x - 1) is equal to zero or undefined.

The expression is undefined when the denominator is equal to zero:

5x - 1 = 0

x = 1/5

The expression is equal to zero when the numerator is equal to zero:

x + 8 = 0

x = -8

Therefore,

The critical values are x = -8 and x = 1/5.

Step 2:

Create a sign chart to determine the sign of the expression (x + 8)/(5x - 1) for each interval between the critical values.

On the interval (-∞, -8), the expression (x + 8)/(5x - 1) is negative if x + 8 is negative, which means x < -8.

On the interval (-8, 1/5), the expression (x + 8)/(5x - 1) is positive if both the numerator and denominator are negative, or if both are positive.

The numerator is negative on this interval, so the expression is positive if the denominator is negative, which means x < 1/5.

On the interval (1/5, ∞), the expression (x + 8)/(5x - 1) is negative if the numerator is negative and the denominator is positive, which means x > 1/5.

Step 3:

Write the solution in interval notation.

Therefore,

The solution to the inequality (x + 8)/(5x - 1) ≤ 0 is:

x ∈ (-∞, -8] ∪ [1/5, ∞)

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Answer:

50% discount

Step-by-step explanation:

Given the following question:

50% of 32

To find the answer we will use the formula to calculate percentages, and then solve by subtracting the answer from the initial cost of the sneakers.

[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{50\times32}{100}[/tex]
[tex]50\times32=1600[/tex]
[tex]1600\div100=16[/tex]
[tex]=16[/tex]

Or...

[tex]32\div2=16[/tex]
[tex]=16[/tex]

50% of 32 is 16 which means the shoes has a "50% discount."

Hope this helps.

Answer:

$28.80

Step-by-step explanation:

32 x 0.1 = 3.2
32 - 3.2 =28.8

Hope this helps :)

Answer:

$28.8

Step-by-step explanation:

10% of 32 is 3.2

32 - 3.2 = 28.8

Answer:

The theoretical probability states that it should be equal. That is should be 50/50 but the experimental results show that the coin favoured heads.

Quadrilateral ABCD was rotated 180 degrees about the origin to form A'B'C'D. The two figures are congruent to each other.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Quadrilateral ABCD was rotated 180 degrees about the origin to form A'B'C'D. The two figures are congruent to each other.

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Hence, required answer is 336

See the picture for the solution

Answer:

Shown above

Step-by-step explanation:

Sorry for my untidy handwriting

Answer:

B. x > 4

Step-by-step explanation:

12 < 8 + x

12-8 < 8-8 +x

12-8 < x

4 <x

x > 4

Answer:

D Because other options do not have integration constants

Answer:

The answer is b) 3y-4

Step-by-step explanation:

Answer:

No, I do not agree. This is because 10⁰ is equivalent to 1.

Step-by-step explanation:

any number to the power of 0 is equal to 1

Answer:

The correct answer is -30

Step-by-step explanation:

4(x+32)=8 basically you multiply 4 times the numbers that are in the parentesis which that will equals to 4x+128 because 4x1= 4x and 4x32 = 128. then you subtract 128 from 8 which equals to -120. you divide -120 by 4 which equals to -30.

Step-by-step explanation:

a) Perimeter is equal to 2w + 2L

2(3x + 4) + 2(x + 3)

6x + 8 + 2x + 6

8x + 14

b) Put 5 in x's place

8×5 + 14

40 + 14

54

c) Area = (3x + 4) * (x + 3)

Put 4 in x's place

(3×4 + 4) * (4 + 3)

12 + 4 * 7

16 * 7

112

Answer:

  8 11/20 ft³

Step-by-step explanation:

For dilated figures, the ratio of volumes is the cube of the ratio of corresponding linear dimensions.

  Vn/Vm = (Hn/Hm)³

  Vn = Vm(Hn/Hm)³ = (68 2/5 ft³)((2 3/8 ft)/(4 3/4 ft))³

  Vn = (342/5 ft³)((19/8)/(19/4))³ = (342/5 ft³)(1/2)³ = 342/40 ft³

  Vn = 8 11/20 ft³

The volume of Prism N is 8 11/20 ft³.

Answer:

The answer is 8 11/20.

Answer:

  (3√26, 0)

Step-by-step explanation:

Finish your work by evaluating the sine and cosine. The imaginary part corresponds to the y-coordinate in (x, y) form.

  3√26(cos(360°) +i·sin(360°)) = 3√26(1 +0i)

In rectangular form, that is ...

  (3√26, 0)