All but 36 of the 120 state capitals have an interstate highway serving them. What percent of the capitals do not have interstates?

The area of the shaded region is 51.75 in².

From the figure

Radius of semicircle = √25² - 20²

                                  =√625-  400 = 15 inch

Now, Area of Trapezium = 1/02 ( a +b ) h

= 1/2 (17 + 37) x 15

= 1/2 (54) x 15

= 27 x 15

= 405 in²

Then, Area of Shaded region

= Area of Trapezium -  Area of semicircle

= (405 - πr²)

= 405 - 353.25

= 51.75 in²

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The area of a shape is calculated by calculating the amount of space on the shape

By definitinon, the area of a shape is the amount of space on the shape

using the above as a guide, we have the following:

There are several formulas to calculate area

The formula to use is dependent on the shape whose area is being calculated

This means that the area of trapezoid cannot be calculated using the area of parallelogram

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All the numbers are rational numbers.

We have,

Rational numbers are those numbers that are terminating and recurring non-terminating.

Irrational numbers are those numbers that are non-terminating and non-recurring.

The numbers are:

1)

0.020202

This is non terminating recurring number.

It is a rational number.

2)

0.8

This is a terminating number.

It is a rational number.

3)

0.020202

This is non terminating recurring number.

It is a rational number.

Thus,

All the numbers are rational numbers.

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2nd and 4th is correct. Hope you got it!

The solutions to this quadratic equation are x = √(73/3) + 5 or x = -√(73/3) + 5.

In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

3x² - 30x = -2

By dividing all through by 3, we have:

x² - 10x = -2/3

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = -2/3 + (-10/2)²

x² - 10x + 25 = -2/3 + 25

x² - 10x + 25 = 73/3

By simplifying, we have;

(x - 5)² = 73/3

x = √(73/3) + 5 or x = -√(73/3) + 5

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Answer:

B.

Step-by-step explanation:

As the steps imply,

The accrued value of the account in 10 years is $641.75

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Amount = P * (1 + 0.25r)ᵗ

Where

P = Principal = 600

r = Rate = 2.7% = 0.27

t = time = 10

Substitute the known values in the above equation, so, we have the following representation

Amount = 600 * (1 + 0.25 * 0.27)¹⁰

Evaluate

Amount = 641.75

Hence, the amount is 641.75

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Answer:

[tex]30d^2[/tex]

Step-by-step explanation:

Answer:

90% of 300 = .90 × 300 = 270 high- definition televisions on order.

The transformation of f(x) that will produce g(x) is given as follows:

g(x) = f(x)/4.

If we observe at the table, we have that each value of g(x) is one fourth of the value of the function f(x).

Hence the transformation of f(x) that will produce g(x) is given as follows:

g(x) = f(x)/4.

The transformation means that the function g(x) is a vertical compression by a factor of 4 of the function f(x).

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Answer:

Step-by-step explanation:

f(x)=2x

note: putting anything in the f(x) parentheses replaces x in the function with that value

so,

f(-3) = 2(-3) = -6

f(0) = 2*0 = 0

f(2) = 2(2) = 4

The actual rocket height is 1080 inches and the height of the actual rocket is 90 feet.

If the 1/20 scale model of the rocket stands 54 inches high, we can find the height of the actual rocket by multiplying the height of the model by 20:

Actual rocket height = 54 inches x 20 = 1080 inches

In order to convert inches to feet, we divide by 12:

Actual rocket height = 1080 inches / 12 = 90 feet

Therefore, the height of the actual rocket is 90 feet.

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The 1/20 scale model of the rocket stood 54 inches high What was the height of the actual rocket?

(b) Find the height of the actual rocket in feet.

Answer:

S = 2π(14^2) + 2π(14)(154)

= 2π(196) + 2π(2,156)

= 4,704π = 14,778.1 ft^2

Using 3.14 for π:

S = 4,704(3.14) = 14,770.6 ft^2

The equation 5ʷ ⁺ ³ = 17 when solved for w is approximately w = 0.41

From the question, we have the following parameters that can be used in our computation:

5ʷ ⁺ ³ = 17

Take the logarithm of both sides of the equation

So, we have

w + 3 = ln(17)/ln(3)

Evaluate the quotient on the left side of the equation

This gives

w + 3 = 2.59

So, we have

-3 + w + 3 = 2.59 - 3

Evaluate

w = 0.41

Hence, the equation when solved for w is approximately w = 0.41

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Answer:

The value of the account will be $5,628

Step-by-step explanation:

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have    

substitute in the formula above  

therefore

The value of the account will be $5,628

Answer:

25

Step-by-step explanation:

To solve this problem you have to use this formula [tex](\frac{b}{2})^{2}[/tex] it. So in this case b is the term next to the x term. This number is 10. So all we have to do is insert it into the formula. This would give us:

[tex]=(\frac{10}{2})^{2}\\\\=(5)^{2}\\\\= 25[/tex]

The constant term is 25.

Could I get Brainilest, please? I'm trying to get to the expert level

Answer:

$30.25

Step-by-step explanation:

55% of 55$ is $30.25. she wants 45 % off of 55$. which is $24.75. 55-24.75 is 30.25

$30.25

since it's 45% off, you need to subtract 45% from 100%

100%-45%=55%

then turn the % into a decimal

55%/100=0.55

now multiply the original price by 0.55

0.55*55=30.25

Answer:

351 cm^3

Step-by-step explanation:

The base of a right prism ABC is an isosceles triangle with AB = BC and m∠ACB 35°. The diagonal of lateral face ABA is 18 cm and m∠BAB = 50°. Find the volume of the prism. Round your answer to the nearest cm

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Let AB = BC = x be the base of the isosceles triangle ABC. Then, the third side AC is:

AC = 2x * sin(35°)

Using the sine rule in triangle ABA, we have:

AB / sin(50°) = 18 / sin(80°)

Solving for AB, we get:

AB = 18 * sin(50°) / sin(80°)

The height of the prism is AB * cos(35°). Therefore, the volume of the prism is:

V = (1/2) * x^2 * 2x * sin(35°) * AB * cos(35°)

Substituting the values we have calculated, we get:

V = (1/2) * x^2 * 2x * sin(35°) * [18 * sin(50°) / sin(80°)] * cos(35°)

V ≈ 351 cm^3

Therefore, the volume of the prism is approximately 351 cubic centimeters.

The expression for the number of cookies Anna has left is [tex]3c - 8[/tex].

An expression refers to statement that have minimum of two numbers or variables or both and an operator connecting them.

The total number of cookies Anna baked is:

= 3 batches * c cookies/batch

= 3c cookies

After eating 8 cookies, Anna has left:

= 3c cookies - 8 cookies

So, the expression for the number of cookies Anna has left is [tex]3c - 8[/tex].

Full question "Anna baked 3 batches of cookies with c cookies in each batch she then ate 8 cookies. How many cookies does anna have left write your answer as an expression.

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The probability that either event will occur is 7/25

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 which is equivalent to 100% in percentage.

Probability = sample space /Total outcome

P(A or B) = P(A) +P(B) -P(A and B)

The total element = 25+5+15+5 = 50

therefore total outcome = 50

P(A) = 25/50

P(B) = 15/50

P(A and B) = 5/40

Therefore P(A and B) = 25/50+15/50 - 5/50

= 35/50 = 7/25

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A graph of the reflection of line segment AB is shown on the coordinate plane below.

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative.

Furthermore, a reflection across the line y = x would interchange (switch) the x-coordinate and y-coordinate and this is represented by the following transformation rule:

(x, y)                                    →              (y, x)

Ordered pair A = (4, -1)    →        Ordered pair A' = (-1, 4).

Ordered pair B = (4, 5)    →        Ordered pair B' = (5, 4).

In this exercise, we would use an online graphing calculator to plot the image of line segment AB after a reflection about the line y = x.

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The solution for x is -48, the answer is D) -48.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It represents a value that can change based on the values assigned to the variables.

Starting with:

x:4 = 12

Multiplying both sides by -1 gives:

(-x÷4) = -12

Simplifying the left side:

x÷4 = -12

Multiplying both sides by 4 gives:

x = -48

Therefore, the solution for x is -48, the answer is D) -48.

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Answer:(a) The rate of decay is 14.4% per day, which can be written as a decimal by dividing by 100: r = 0.144.

(b) The formula for continuous decay is given by:

A = A₀ * e^(-rt)

where A is the remaining amount of the substance after time t, A₀ is the initial amount, r is the rate of decay, and e is the mathematical constant approximately equal to 2.71828.

Plugging in the given values, we get:

A = 140 * e^(-0.144*15)

A = 140 * e^(-2.16)

A ≈ 47.23

Therefore, after 15 days, approximately 47.23 mg of the radioactive substance will be left, rounded to two decimal places.

Step-by-step explanation:

The probability of rolling a 4 on a single throw of a fair 6-sided die is 1/6, since there is only one way to roll a 4 and there are 6 equally likely outcomes in total.

The probability of rolling an even number on a single throw of a fair 6-sided die is 3/6, or 1/2, since there are three even numbers (2, 4, and 6) out of six possible outcomes.

To find the probability of rolling a 4 or an even number on a single throw, we can add the probabilities of these two events:

P(4 or even) = P(4) + P(even) - P(4 and even)

where P(4 and even) is the probability of rolling a 4 and an even number on the same throw. Since there is only one outcome (rolling a 4), which is not even, this probability is 0.

Therefore:

P(4 or even) = P(4) + P(even) - P(4 and even)

             = 1/6 + 1/2 - 0

             = 2/3

So the probability of rolling a 4 or an even number on a single throw of a 6-sided die is 2/3.

If the die is thrown 2 times, the probability of rolling a 4 or an even number on both throws is the product of the probabilities of rolling a 4 or an even number on each throw:

P(4 or even on both throws) = P(4 or even) × P(4 or even)

                           = (2/3) × (2/3)

                           = 4/9

Therefore, the probability of rolling a 4 or an even number on both throws of a 6-sided die is 4/9.

B = (715x) / (h^2)

Step 1: Get rid of the denominator by multiplying both sides by h^2

(B)(h^2) = 715x

Step 2: Isolate x by dividing both sides by 715

(Bh^2) / 715 = x

Answer: x = Bh^2 / 715

Hope this helps!

Rounding to three decimal places, the confidence interval is (0.419, 0.574).

The sample proportion, p′ = 0.842, which is the point estimate of the population proportion, must be determined in order to calculate the confidence interval. Given that CL = 0.95 is the requested confidence level, = 1 - CL = 1 - 0.95 = 0.05 ( 2) ( 2) = 0.025.

Confidence interval=proportion±margin of error

CI = p ± ME

The proportion is:

p = x / n

p = 55/110

p = 0.5

Margin of error=critical value × standard error

ME = CV × SE

n > 30, so we can approximate CV with a normal distribution.

At P=88%, CV=1.55.

SE = √(pq / n)

SE = √(0.5 (1−0.5)/110)

SE = 0.048

So the margin of error is:

ME = 1.55 × 0.048

ME = 0.074

So the confidence interval is:

CI = 0.5 ± 0.074

CI = (0.426, 0.574)

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Question:

Use the given degree of confidence and Sample data to construct income confidence interval for the population proportion p. n=110, x=55; 88% confidence

A) 0.426 B)0.442 C)0.425 D)0.421