The daily listening audience of an AM radio station is four times as large as that of its FM sister station. If 105,000 people listen to these two radio stations, how many listeners does the FM station have?

Answer:

  8

Step-by-step explanation:

You want to know the measure of segment XY if ∆XYZ ≅ ∆MNL and MN = 8.

Segment XY is named using the first two vertices listed in the name of ∆XYZ. That means the segment is the same length as the one named by the first two vertices listed in the name of congruent ∆MNL, segment MN.

Segment MN is given as 8 units long. Segment XY is congruent, so is also 8 units long.

  XY = 8 units

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Answer: 15cm

Step-by-step explanation: If the length of the model on the top is 6 cm, then the length of the model on the bottom must be 15 cm

\(\\ \tt\hookrightarrow UW=UY\)

\(\\ \tt\hookrightarrow 2s-35=s\)

\(\\ \tt\hookrightarrow 2s-s=35\)

\(\\ \tt\hookrightarrow s=35\)

Answer:

Step-by-step explanation:

We know that:

Solution:

Hence, the value of s must be 35 units so that the quadrilateral becomes a parallelogram.

Answer:only if all of the terms in the two expressions are the same, then the two expressions are similar

As per the given ratio Mina's age is 12 years old.

Ratio in math is defined as shows how many times one number contains another.

Here we have given ratio information as written as

=> Lev's age : Mina's age = 1 : 2

And the ratio between is written as

=> Mina's age : Naomi's age = 3 : 4

Here we have given the condition that the sum of all three ages is written as,

=> Lev + Mina + Naomi = 30 to 50

Here let us consider Lev's age as L, Mina's age as M and Naomi's age as N

Then the ratio is calculated as,

=> L = 1/2M

=> N = 4/3M

And the sum of all value is written as

=> L + M + N = 30 to 50

When we apply the values on it, then we get,

1/2M + M + 4/3M = 30 to 50

When we simplify it by multiply all by 6, then we get

=> 3M + 6M + 8M = 180 to 300

=> 17M = 180 to 300

Therefore, here we have to find a number between 180 and 300 that divisible by 17 and 6.

So let us consider that that number is 204.

Then the value of M is calculated as,

=> 17M = 204

=> M = 12

Complete question:

Let us consider that suppose the ratio of lev's age to mina's age is 1 : 2 and the ratio of mina's age to Naomi's age is 3 : 4. if the sum of all three ages is between 30 and 50, then how old is mina?

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Answer: 43516

Step-by-step explanation:

C =(Current Salary). C x .012( 12%)=516

C + 516 = 43516

Answer:

-0.33333333333 in other word it o.3 with line over 3

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

y = a^x

1/16 = a^2

so the answer is 1/4

Answers:

1. y=4x+15

1. y=4x+152.y=×-9

Add them both up and divided by 2, 52+45=97. 97/2 =48.5

Step-by-step explanation:

Answer: $41.32

Step-by-step explanation:

1. Figure out how many students need cookies.

26 + 31 = 57, 57 students need cookies, thus they need to make at least 57 cookies.

2. Figure out which ingredients are still needed.

One tub of cookie dough makes 20 cookies, so to make 57 cookies, they will need at least three tubs. One frosting tin covers 30 cookies, so to cover 57 cookies, they will need at least two tins. One bag of sprinkles covers 60 cookies, so they will only need one bag, as 60 > 57.

3. Tally up the prices of each ingredient

Price of cookie dough = 9.95, amount of cookie dough needed = 3

9.95 * 3 = 29.85

Price of frosting = $4.59, amount of frosting needed = 2

4.59 * 2 = 9.18

Price of sprinkles = 2.29, amount of sprinkles needed = 1

2.29 * 1 = 2.29

4. Find the sum.

29.85 + 9.18 + 2.29 = 41.32

Answer:

The answer to your problem is, 1.20

Step-by-step explanation:

First we need to convert our fraction to decimal which is:

1.2 EXACT.

We already know that it is in the tenths place shown: 1.2

We know that but how do you round it to the hundredths place?

Short answer: Cannot really since it is in the tenths place we can technically round it to, 1.20. Same fraction by the way.

Thus the answer to your problem is, 1.20

Exact value:  \(c = \frac{-11+\sqrt{165}}{22}\)

Approximate value:    c = 0.08387

Round the approximate value however you need to

==============================================

Work Shown:

Let x = 1+c

\(\displaystyle S = \sum_{n=2}^{\infty}(1+c)^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}x^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}\frac{1}{x^n}\\\\\\\displaystyle S = \frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^4}\ldots\\\\\\\)

We have an infinite geometric series here. The first term is a = 1/(x^2). The common ratio is r = 1/x.

Each new term is found by multiplying the previous term by 1/x.

Assuming -1 < r < 1 is true, the infinite geometric sum is

\(S = \frac{a}{1-r}\\\\\\S = \frac{1/x^2}{1-1/x}\\\\\\S = \frac{1/x^2}{x/x-1/x}\\\\\\S = \frac{1/x^2}{(x-1)/x}\\\\\\S = \frac{1}{x^2}\div\frac{x-1}{x}\\\\\\S = \frac{1}{x^2}*\frac{x}{x-1}\\\\\\S = \frac{1}{x^2-x}\\\\\\\)

Plug in S = 11 and solve for x

\(S = \frac{1}{x^2-x}\\\\11 = \frac{1}{x^2-x}\\\\11(x^2-x) = 1\\\\11x^2-11x = 1\\\\11x^2-11x-1 = 0\\\\\)

Use the quadratic formula to find the two solutions

\(x = \frac{11+\sqrt{165}}{22} \approx 1.08387\\\\x = \frac{11-\sqrt{165}}{22} \approx -0.08387\\\\\)

Using these x values, we find that the corresponding r values are

r = 1/x = 1/(1.08387) = 0.92262

r = 1/x = 1/(-0.08387) = -11.92321

The first r value makes -1 < r < 1 true, but the second r value does not. So we will be ignoring the solution x = -0.08387

----------------------------------------------

Using the solution that corresponds to x = 1.08387, we find the value of c is

\(x = c+1\\\\c = x-1\\\\c = \frac{11+\sqrt{165}}{22}-1\\\\c = \frac{11+\sqrt{165}}{22}-\frac{22}{22}\\\\c = \frac{11+\sqrt{165}-22}{22}\\\\c = \frac{-11+\sqrt{165}}{22}\\\\c \approx 0.08387\\\\\)

4 he can make four cuAse u can cut 8/10s into 4)5

Answer:

4

Step-by-step explanation:

Answer:

1050

Step-by-step explanation:

I'm pretty positive it would be 1050 by multiplying 50 and 20 and adding 50

The total number of seats in the auditorium are 2225.

Given is that an auditorium has 50 rows of seats. The first row has 20 seats, the second row has 21 seats, the third row has 22 seats.

We can write the sequence as -

20, 21, 22, 23, 24, .......,

It is a arithmetic sequence. We can write the total number of seats in the auditorium as the sum of the terms of the sequence. We can write -

S{n} = (50/2)(2 x 20 + 49 x 1)

S{n} = 25(40 + 49)

S{n} = 25 x 89

S{n} = 2225

Therefore, the total number of seats in the auditorium are 2225.

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To solve the exercise, we can use the following rule of transformation of functions:

In this case, we can see that the graph of f(x) shrinks by a factor of 2, because:

Therefore, the equation of g in terms of f is:

The Area of Square is 81 cm².

let the side of the square which is length for both rectangles be a.

let the width of rectangle be x and y.

So, x+ y= a

sum of perimeters= 54

2 (a +x ) + 2 (a+ y) = 54

2a+ 2x + 2a+ 2y = 54

2a + 2a + 2(x+ y) = 54

4a + 2 (a) = 54

4a + 2a = 54

6a = 54

a= 54/6

a= 9

So, area of square

= 9 x 9

= 81 cm²

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Answer:

c because you dont need the extra zero on the 8

Sara needs to reduce the price by approximately 33.33% to provide the same value for money as Zak's idea.

To find the percentage by which Sara needs to reduce the price to provide the same value for money as Zak's idea, we need to compare the original price and the new price under Zak's idea.

Let's assume the original price of a box of pet food is P and the original amount of pet food in each box is A.

According to Zak's idea, the company will put 50% more pet food into each box without changing the price. Therefore, the new amount of pet food in each box will be 1.5A.

To calculate the value for money under Zak's idea, we divide the amount of pet food by the price:

Value for money (Zak's idea) = (1.5A) / P

Now, let's consider Sara's idea. She wants to reduce the price but keep the amount of pet food unchanged. Let's assume Sara reduces the price by a percentage represented by x.

Under Sara's idea, the new price of a box of pet food will be P - (x/100)P = P(1 - x/100).

Since Sara wants her idea to provide the same value for money as Zak's idea, we can equate the two value for money expressions:

(1.5A) / P = (A) / (P(1 - x/100))

Cross-multiplying and simplifying the equation:

1.5A * P(1 - x/100) = A * P

1.5(1 - x/100) = 1

Simplifying further:

1 - x/100 = 2/3

-x/100 = -1/3

x/100 = 1/3

x = 100/3

Therefore, Sara needs to reduce the price by approximately 33.33% to provide the same value for money as Zak's idea.

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Using the cosine ratio, the distance between Dimitri and Sarah is calculated as approximately 12.4 m.

The cosine ratio is a trigonometric ratio that represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. It is calculated by dividing the length of the adjacent side by the length of the hypotenuse.

Using the cosine ratio, we have:

Reference angle (∅) = 72 degrees

Hypotenuse length = 40 m

Adjacent length = distance between Dimitri and Sarah = x

Plug in the values:

cos 72 = x/40

x = cos 72 * 40

x ≈ 12.4 [to one decimal place]

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Answer:

f(3x + 1) = - 18x - 5

Step-by-step explanation:

Substitute x = 3x + 1 into f(x), that is

f(3x + 1)

= - 6(3x + 1) + 1 ← distribute and simplify

= - 18x - 6 + 1

= - 18x - 5

Answer:

(x + i) (x - i)

Step-by-step explanation:

The expression x^2 + 1 is a sum of squares, which means that it cannot be factored using real numbers. However, it can be factored using complex numbers.

To factor x^2 + 1, we can use the fact that i^2 = -1, where i is the imaginary unit.

We can rewrite x^2 + 1 as:

x^2 + 1 = x^2 - (-1)

Now, we can use the difference of squares formula to factor x^2 - (-1):

x^2 - (-1) = (x + i)(x - i)

Therefore, the factored form of x^2 + 1 is:

(x + i)(x - i)

Answer:

48

Step-by-step explanation:

4*2*3 for the 4 flaps

2*4*3 for the 2 tops

(4*2*3) + (2*4*3) = 48

Answer:

52 square inches

Step-by-step explanation:

to find the surface area of a rectangular prism the formula is

S.A.=2(l*w+l*h+w*h)

2(4*3+4*2+3*2)

=52 square inches

here l is length w is width and h is height

Answer:

99.7%

Step-by-step explanation:

Empirical rule formula states that:

• 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

From the question, we have mean of 98.18 F and a standard deviation of 0.65 F

The approximate percentage of healthy adults with body temperatures between 96.23 F and100.13 ​F is

μ - 3σ

= 98.18 - 3(0.65)

= 98.18 - 1.95

= 96.23 F

μ + 3σ.

98.18 + 3(0.65)

= 98.18 + 1.95

= 100.13 F

Therefore, the approximate percentage of healthy adults with body temperatures between 96.23 F and 100.13 ​F which is within 3 standard deviations of the mean is 99.7%

The length of BD is 22.

In the given scenario, let's consider the following information.

AD = 8

AE = 6

EC is 12 more than BD.

To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.

From the given information, we know that AD = 8 and AE = 6.

Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.

First, let's find the intercepted arc corresponding to AD:

Intercepted Arc ADB = 2 \(\times\) AD = 2 \(\times\) 8 = 16

Similarly, we can find the intercepted arc corresponding to AE:

Intercepted Arc AEC = 2 \(\times\) AE = 2 \(\times\) 6 = 12

Now, we know that EC is 12 more than BD.

Let's assume the length of BD as x.

BD + 12 = EC

Now, let's consider the intercepted arcs theorem:

Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C

16 - 12 = Angle B - Angle C

4 = Angle B - Angle C.

Since Angle B and Angle C are vertical angles, they are congruent:

Angle B = Angle C.

Therefore, we can say:

4 = Angle B - Angle B

4 = 0

However, we have reached an inconsistency here.

The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.

As a result, we cannot determine the length of BD based on the given information.

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Answer:

43 students were in each bus

Step-by-step explanation:

Total students: 395

Students travelled in cars: 8

Students travelled in buses: 395-8=387

Number of buses filled:9

Number of students in each bus: 387÷9=43

Answer:

1. 16%

2. The middle 95% of newborn babies weigh between 6.2 and 9 pounds.

3. 2.5%

4. Approximately 50% of newborn babies weigh more than 7.6 pounds.

5. 83.85%

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 7.6 pounds, standard deviation of 0.7 pounds

1. What percent of newborn babies weigh more than 8.3 pounds?

7.6 + 0.7 = 8.3.

So more than 1 standard deviation above the mean.

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

Of those above the mean, 100 - 68 = 32% are more than one standard deviation above the mean. So

\(0.32*0.5 = 0.16\)

16% of newborn babies weigh more than 8.3 pounds.

2. The middle 95% of newborn babies weigh between and pounds.

Within 2 standard deviations of the mean, so:

7.6 - 2*0.7 = 6.2 pounds

7.6 + 2*0.7 = 9 pounds.

The middle 95% of newborn babies weigh between 6.2 and 9 pounds.

3. What percent of newborn babies weigh less than 6.2 pounds?

More than 2 standard deviations below the mean, which is 5% of the 50% below the mean, so:

\(p = 0.05*0.5 = 0.025\)

2.5% of newborn babies weigh less than 6.2 pounds.

4. Approximately 50% of newborn babies weigh more than pounds.

Due to the symmetry of the normal distribution, the mean, so 7.6 pounds.

Approximately 50% of newborn babies weigh more than 7.6 pounds.

5. What percent of newborn babies weigh between 6.9 and 9.7 pounds?

6.9 = 7.6 - 0.7

9.7 = 7.6 + 3*0.7

Within 1 standard deviation below the mean(68% of the 50% below) and 3 standard deviations above the mean(99.7% of the 50% above). So

\(p = 0.68*0.5 + 0.997*0.5 = 0.8385\)

83.85% of newborn babies weigh between 6.9 and 9.7 pounds.

Answer:

Step-by-step explanation: