An exponent is always smaller in value than the base. true/false

Answer:

B, C

Step-by-step explanation:

√16 = 4 and √64= 8

so if √16 / √64,

then 4/8

lastly, 4/8 equals to 1/2

you can find this because 4 goes into 4 and 8 so 4/4=1 and 8/4=2

so 1/2

hope this helps :)

a) Option D, (39,43) could be the 99% confidence limit.

b) The determined minimum sample size is 166.

a) For a given sample size, the confidence interval is just the range of values including the real population mean. The confidence interval is interpreted as follows:

The real population mean are contained in around 95% of the estimated confidence intervals.

The breadth of the interval and the confidence level (including 95% or 99%) have a positive connection.

As the confidence level rises, the range of both the confidence interval expands, implying that the lower limit of the interval shrinks and the top bound of the interval expands.

Option B is the correct one among the available possibilities since it entirely follows the pattern. When compared to a 99% confidence interval, 33 should be less than 34, and 46 is more than 43.

b) s = Standard Deviation = $7,500 m = Margin of Error = $1,500 z = Empirical z-score at 95% CI = 2.575

The random sample for a 95% confidence interval is calculated as follows:

= (Z × s)² ÷ m²

= (2.575 × s)² ÷ m²

= (2.575 × 7500)² ÷ (1500)²

= 165.76

≈ 166

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answers:

1. 92,862

2. 9,774

3. 60,750

4. 60,705

5. 42,581

its in order like u put it in THE SAME ORDER.

Answer:

Step-by-step explanation:

For number 8 the answer is y=2x+7 because our equation is y+1=2(x+4) distribute the 2 to get y+1=2x+8 and you then do inverse operation by subtracting the 1 on both sides to get y=2x+7 and the slope intercept form is y=mx+b so that’s why

for number 9 the answer is (0,7) as to find the y-intercept, substitute in 0 for x and solve for y as y+1=2((0)+4) distribute the 2 after doing 0+4 to get y+1=8 inverse operation so subtract 1 to get 7 so that’s why it’s (0,7)

and for 10 the answer is 2x−y=−7

The domain and range of the of this function C(n) = 120 + 8n, in the context of the situation is 10 ≤ n ≤ 24 and 200 ≤ C ≤ 312 respectively.

The set of inputs a function can accept is referred to as the domain of the function in mathematics. DOM (f) or DOM f, where f is the function, may be used to indicate it.

A function f: X to Y has X as its domain, to put it more precisely. The domain of a function is not a property of it, but rather a part of the definition in contemporary mathematical terminology.

The function f can be represented graphically using the Cartesian coordinate system in the unique situation where X and Y are both subsets of R. A projection of the function's graph onto the graph's x-axis in this instance serves as the domain's representation.

We have given the function C(n) = 120 + 8n where n is no. of children going to trip which must be at least 10 and function C is the total cost trip.

If at least 10 children must go to make the trip possible, then n must be greater than 10 and the total no. of children is 24 which gives us

10 ≤ n ≤ 24, n is restricted between 10 and 24

Also, if n is at least 10, the putting the value in the function C(n) = 120 + 8n gives us

C(n) = 120 + 8(10)

      = 200

Which means C must be greater or equal to 200 but we also take the condition in consideration that all students are going to the trip meaning 24 children is n, which gives us

C(n) = 120 + 8(24)

      = 312

This gives us, 200 ≤ C ≤ 312, that is C is restricted between 200 and 312.

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The value of the constant of proportionality k = 36

The Direct Variation :

Direct Variation is said to be the relationship between two variables in which one of the variables is multiple of the other variable.

When x is directly proportional to y then the relation can be written as  

= >  x ∝ y  

=>   x = ky  [ here k is constant value ]

Here we have,

The number of words Latisha can text 'y' is varies directly with 'x' the number of minutes spent texting

Here, y = 180  and  x = 5

From the above data,  

=>  180 = k (5)  

=> k = 180/5 = 36

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Answer:

The answer is 56 yards

Step-by-step explanation:

Im sorry I'm not smart enough to answer I just look around for it but I'm sorry I can't explain.

Answer:

3.2

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

LCM of 16 and 40 is 80. Among all common multiples of 16 and 40, the LCM of 16 and 40 is the smallest number. (16, 32, 48, 64, etc.) and (40, 80, 120, 160, 200, 240, etc.)

The coordinates of y-intercept are [tex](0,10)[/tex]

What is the y-intercept of a function?

When a graph crosses the y-axis, that location is known as the y-intercept. It is the value of y at x=0, to put it another way.

We are given a function [tex]y=x^{2} -15x+10[/tex].

We have to find the y-intercept of the above function.

to find that we put [tex]x=0[/tex] in the above function we get,

[tex]y=x^{2} -15x+10\\y=0^{2}-15(0)+10\\ y=10[/tex]

The coordinates of y-intercept can be given as [tex](0,10)[/tex].

Hence the coordinates of y-intercept are [tex](0,10)[/tex].

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ANSWER :

D.

EXPLANATION :

From the problem, we have a graph that goes to positive infinity as x goes to the positive infinity.

Note that in an exponential function :

The function goes to positive infinity if "a" is greater than 1

The function goes to negative infinity if "a" is less than 1

Since the given graph goes to positive infinity, we are looking for the function whose "a" is greater than 1.

We have Options A and D.

Next is to check the y-intercept.

The graph intersects the y-axis at (0, -3)

Substitute x = 0 and f(x) should be -3

For Option A :

For Option D :

Therefore, the answer is D.

Answer:

The area is 426 square feet.

Expansion of (x + 3) (x + 5)   [tex]=x^{2} +8x+15[/tex]

How is  the expansion done?

Applying the Product of binomials rule,

(x+a) (x+b) = [tex]x^{2} +(a + b)x +ab[/tex]

Here, in the given expression:

a = 3 and b = 5

[tex](x + 3) (x + 5) =x^{2} +(3 + 5)x +15\\\\ =x^{2} +8x+15[/tex]

What is the product of binomials rule?

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Solution

Step 1:

Let the other two equal angles be x.

Step 2:

Sum of angles in a triangle is 180 degrees:

Answer

The measure of the other two angles is 67.5

The perimeter of the figure measures 38 inches.

The perimeter will be equal to the sum of the measures of each side of the figure.

We can see that the bottom side measures 13 inches, and also does the top side (where the top side is "broken" into two parts).

Similarly, the right side measures 6 inches, and also does the left side, only that the left side is broken into two parts.

Then the perimeter of the figure is:

P = 13in + 13in + 6in + 6in = 26in + 12in = 38in

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The two values of x in the equation are x = -8 and x = 8

The equation is given as

x² - 14 = 50

Add 14 to both sides of the equation

So, we have the following equation

x² - 14 + 14 = 50 + 14

Evaluate the like terms

So, we have the following equation

x² = 64

Take the square roots of both sides

√x² = ±√64

Evaluate the square roots

So, we have the following equation

x = ±8

Split

x = -8 and x = 8

Hence, the values are x = -8 and x = 8

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The result of the expression [tex]\frac{1}{5^{-1} }[/tex] is 5

The expression is [tex]\frac{1}{5^{-1} }[/tex]

To solve this problem first we have to rearrange the terms and do the arithmetic operations on the expression.

Expressions is the mathematical statements that have a minimum of two terms containing numbers or variables, connected by an operator in between. The operator maybe addition, subtraction, division or multiplication. We have to use this operations on the like terms of the expression. To  solve the mathematical expression we have to do the arithmetic operation on like terms.

The expression is  [tex]\frac{1}{5^{-1} }[/tex]

We know

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

Apply this method in the expression

[tex]\frac{1}{5^{-1} }[/tex] = 5

Hence, The result of the expression [tex]\frac{1}{5^{-1} }[/tex] is 5

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The quantities do not have a proportional relationship because the ratio of the cost to shirts is not equivalent.

The two quantities would have a proportional relationship if the constant of proportionality are equal. The constant of proportionality would be equivalent to the cost of one shirt.

The equation that can be used to determine the constant of proportionality is:

k = y / x

Where:

k = 25 / 2

k = 12.60

k = $36 / 3

k = $12

The quantities are not proportional because the constant of proportionality are different.

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The positive integers (n) for which the perimeter of sector AOB is greater than 20 are 7, 8, 9 and 10. Also, the positive integer (n) for which the perimeter of sector AOB is less than 30 is 11.

The length of an arc of a circle increases as the sector angle increases, provided that the radius of the circle remains the same. Additionally, the ratio of the length of an arc (arc length) of a circle to the circumference of the circle is equal to the ratio of the sector angle to angle measure of a circle (360°).

By applying this ratio to this circle, we would have the following mathematical expression:

Length of arc AB/Circumference = Sector angle/360°

Rearranging the above mathematical expression, we have:

Length of arc AB = (Sector angle/360°) × Circumference

Note: Circumference = πd = π × 2n = 2πn

Sector angle = 360°/n

Substituting the given parameters into the expression, we have;

Length of arc AB = (360°/n/360°) × 2πn

Length of arc AB = 2π

Next, we would calculate the perimeter of sector AOB:

Perimeter of sector AOB = Length of arc AB + AO + OB

Perimeter of sector AOB = 2π + n + n

Perimeter of sector AOB = 2π + 2n

If the perimeter of sector AOB is greater than (>) 20, the positive integers (n) is given by:

P > 20

2π + 2n > 20

2n > 20 - 2π

n > 10 - π

n > 10 - 3.142

n > 6.858 ≈ 6.9.

Therefore, n = 7, 8, 9, and 10.

If the perimeter of sector AOB is less than (<) 30, the positive integers (n) is given by:

P < 30

2π + 2n < 30

2n < 30 - 2π

n < 15 - π

n > 15 - 3.142

n > 11.858 ≈ 11.9.

Therefore, n = 11.

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Given:

Find:-

Value of "q"

Explanation-:

Value of q is:

So,

So, th

Answer:

1 13/20

Step-by-step explanation:

Answer: X= 50

Step-by-step explanation:

To be able to solve this, you must identify vertical angles, as well as a linear pair.

The angle next to the angle of 103 is in a linear pair. This means they both add up to 180.

180- 103 = 77. The angle that is next to the angle of 103 is 77.

You have two angles in a triangle. You can use the triangle sum theorem, which states that all angles of a triangle add up to 180.

180- (53+ 77)= the third angle

180- 130 = 50 (the third angle)

The third angle of the triangle is a vertical angle in relation to x. All vertical angles are equal. This means that x= 50°.

a) The volume of the composite figure is represented by the cubic equation V = x³ + 16 · x.

b) The measure of the missing side x in the composite figure is 3 inches.

a) In the first part of the question we need to derive the volume formula of the composite figure, which is the sum of the volumes of the cube and the rectangular prism:

V = V' + V''

V = x³ + 16 · x, where x is in inches.

The volume is represented by V = x³ + 16 · x.

b) If we know that V = 25 · x, then the measure of the missing side is:

First, set the volume formula found in section a):

V = x³ + 16 · x

Second, replace the volume:

25 · x = x³ + 16 · x

Third, simplify the expression and clear x within the resulting equation by algebra properties:

25 = x² + 16

x² - 9 = 0

x² = 9

x = 3

The measure of the missing side x is 3 inches.

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Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

Let's try solving the equation to the best of our ability before the two variables 'a' and 'b' limit us

       [tex]\text{Copy down the equation}\\2(3x + 5) + ax =5(4x - b)\\\\\text{Multiply the outside constants into the function in the parentheses}\\}6x + 10+ax = 20x - 5b\\\\\text{Let's put the coefficients of the variable on the left-side together in parentheses}\\6x + ax + 10 = 20x - 5b\\(6 + a)x+ 10 = 20x - 5b[/tex]

Now to make the equation works:

              ⇒ [tex]6 + a = 20[/tex]   ⇒ a = 14

              ⇒ -5b = 10      ⇒ b = -2

Answer:

Hope that helps!

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Answer:

Step-by-step explanation:

You want the values of 'a' and 'b' that make 2(3x+5)+ax=5(4x-b) a tautology.

One way to do this is to rewrite the equation in general form. You can do that by subtracting the right-side expression.

  2(3x +5) +ax -5(4x -b) = 0

  6x +10 +ax -20x +5b = 0 . . . . . . eliminate parentheses

  (6 +a -20)x +(10 +5b) = 0 . . . . . . collect terms

This can be made identically zero by making the coefficients be zero.

  6+a-20 = 0 . . . coefficient of x

  a = 14 . . . . . . . add 14 to both sides

and ...

  10 +5b = 0 . . . constant term

  2 +b = 0 . . . . divide by 5

  b = -2 . . . . . . subtract 2 from both sides

To make the expression always true, you must have a = 14, b = -2.

To find the volume of the figure.

volume of the figure=volume of the cone+volume of the rectangle prism.

volume of the figure=72+81=153 inch cube.

about -71 degrees Fahrenheit

branliest?

The area of rectangular is 10 + 8i.

Given,

A rectangular room has lengths and width are 2i and (4 - 5i) respectively.

To find the area of rectangular.

Now, According to the question :

We know that,

Area of rectangular = L x B

where,

L = Length of rectangular

B = Breadth of rectangular

Here, Length and breadth are complex numbers.

and hence, we should remember [tex]i^2[/tex] = -1

Area of Rectangular is = (4 - 5i) x 2i

=8i - 10[tex]i^2[/tex]

= 8i - 10 (-1)

= 8i + 10

Hence, The area of rectangular is 10 + 8i.

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Answer:

Step-by-step explanation:

Because P is located between -8 and -10, your answer would be P=-9. I hope this answered your question!