3) Kevin made $9 per hour working as a
lifeguard. How many hours did he work
this week if his weekly pay before
deductions was $288? Define a variable
and write an equation. Solve the equation.

The total number of bit strings of length 10 over the alphabet {a,b} that have exactly four a's and start with bb or end with bb is 510.

To solve this problem, we can use the principle of multiplication and addition.

First, we need to find the number of bit strings of length 10 with exactly four a's. We can place the four a's in any of the 10 positions, so we have 10 choose 4 (or 10C4) ways to do this. For each of these arrangements, the remaining six positions must be filled with b's, so there is only one way to do this.

Therefore, there are 10C4 = 210 bit strings of length 10 with exactly four a's. Next, we need to count the number of bit strings that start with bb or end with bb.

For bit strings that start with bb, the remaining eight positions can be filled with any combination of a's and b's, so there are 2^8 = 256 such bit strings.

Similarly, for bit strings that end with bb, the first eight positions can be filled with any combination of a's and b's, so there are also 256 such bit strings.

However, we have counted the bit string bbbbbbbbb and bbbaaaaaaa twice (once for each case). Therefore, we need to subtract 2 from the total count.

Thus, the total number of bit strings of length 10 over the alphabet {a,b} that have exactly four a's and start with bb or end with bb is 256 + 256 - 2 = 510.

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To solve the equation we first squared both sides of it, that is:

Now we can use the general formula for quadratic equations, then:

Now that we found two option for x, we have to check which of them is really a solution for the original equation (we have to do this since we squared the original equation to get rid of the root), to do this we plug the values we found to see if the eqaution holds.

If x=1:

hence x=1 is a solution for the original equation.

If x=-2:

since this is not true, x=-2 is not a solution for the original equation.

Therefore, the solution for the equation is x=1.

Answer:

c = 1

Step-by-step explanation:

Given

9 = 2(c + 3) + 1 ← distribute parenthesis and simplify right side

9 = 2c + 6 + 1

9 = 2c + 7 ( subtract 7 from both sides )

2 = 2c ( divide both sides by 2 )

1 = c

Answer:

\(c = 1\)

Step-by-step explanation:

\(9 = 2(c + 3) + 1 \\ 9 = 2c + 6 + 1 \\ 9 = 2c + 7 \\ 9 - 7 = 2c \\ 2 = 2c \\ c = \frac{2}{2} \\ c = 1\)

Answer: 49

Step-by-step explanation:

A=πr^2

A=π(7)^2

A=49π in^2

Answer: 49

Answer:

154 Inches square.

r=7

area= πr^2

= 22/7* 49

= 154

As a decimal 3/5 = 0.6

Multiply the height by 0.6:

1st bounce = 125 x 0.6 = 75

2nd bounce = 75 x 0.6 = 45

3rd bounce = 45 x 0.6 = 27

The answer is 27cm

Answer:

0.6

Step-by-step explanation:

Your welcome and wear a mask :>

Answer:

Step-by-step explanation:

not sure if we're supposed to be dividing, adding or what

Answer:

Step-by-step explanation:

Given that the circumference  of the frame is 56in

we can proceed to obtain the radius of the frame

we know that

circumference= 2πr

56= 2*3.142*r

56= 6.284r

divide both sides by 6.284

r= 56/6.284

r=8.9

approximately radius is 9in

therefore the area of the mirror that is largest would be

Area=  πr^2

Area= 3.142*9^2

Area= 3.142*81

Area= 254.5 in^2

The largest area is 254.5 in^2

Answer:

Obviously B

Step-by-step explanation:

\(e^{-5 \lambda}\) is the probability that we have to wait for more than 5 min for the bus to arrive.

So, \(f_X(x)=\lambda e^{-\lambda x}, x \geq 0\) ⇒ \(P(x \geq 5)=\int_5^{\infty} f_X(x) d x\)

Now, solving the above function as follows:

\(\begin{aligned}&P(x \geq 5)=\int_5^{\infty} f_X(x) d x \\&=\int_5^{\infty} \lambda e^{-\lambda x} d x \\&=\left.\right|_5 ^{\infty} \frac{\lambda e^{-\lambda x}}{-\lambda} \\&=\left.\right|_5 ^{\infty}-e^{-\lambda x} \\&=e^{-5 \lambda}\end{aligned}\)

Therefore, the probability that we have to wait for more than 5 min for the bus to arrive is \(e^{-5 \lambda}\).

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The correct question is given below:
Suppose that the buses arrive are scheduled to arrive at a bus stop at noon are always X minutes late, where X is an exponential random variable with probability density function  \(f_X(x)=\lambda e^{-\lambda x}, x \geq 0\). Suppose you arrive at the bus stop precisely at noon. Find the probability that you have to wait for more than 5 min for the bus to arrive

The option that is not characteristic of the t-test is "The Student t distribution has mean of t = 0 and a standard deviation of 5 = 1". The correct answer is option A.

The t-test is a statistical test that uses the Student t-distribution. The Student t-distribution has a mean of 0, but its standard deviation is not equal to 1. The standard deviation of the t-distribution varies depending on the degrees of freedom, which is determined by the sample size. Therefore, the statement in option A is not true. The correct answer is option A.

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Answer:

Janice travelled 6 miles.

Step-by-step explanation:

23 -5=18

18/3=6

so Janice travelled 6 miles.

The answer of the given figure in the question is, the value of  EH is equal to 15 units.

Proportion is a statement that two ratio (or fractions) are equal. A proportion compares two or more quantities with the same units of measurement.

It can be written in different ways, but the most common is using the colon symbol or a fraction bar.

Since ABCD~EFGH, we know that the corresponding sides are proportional. That is:

AB/EF = AD/EH

Substituting the given values:

5/EH = 4/12

Cross-multiplying:

4EH = 60

Dividing both sides by 4:

EH = 15

Therefore, EH is equal to 15 units.

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In 2013, an Ipsos Global poll conducted for Reuters News found that 63% of 1,000 Canadians supported the legalization of same-sex marriage, who support legalization is 50%, and the alternative hypothesis (Ha: pi not = 0.50) that suggests the population proportion is different from 50%.

a) The standard error measures the variability or uncertainty of the sample proportion compared to the true population proportion. It can be calculated as the square root of (pi * (1 - pi)) divided by the sample size. In this case, the standard error would be computed to estimate the proportion of Canadians who support same-sex marriage.

b) To test the hypothesis, we need to calculate the test statistic. The test statistic for this scenario is the z-score, which is calculated by subtracting the hypothesized population proportion from the sample proportion and dividing it by the standard error. This provides a measure of how many standard errors the observed proportion differs from the hypothesized proportion.

c) By determining the test statistic, we can find the associated p-value. The p-value represents the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. If the p-value is less than the significance level (e.g., 0.05), we can reject the null hypothesis. In this context, the p-value would indicate the strength of evidence against the claim that the population proportion is 50%.

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ANSWER:

STEP-BY-STEP EXPLANATION:

According to the graph, the sum of these two angles is equal to 78°, therefore, the equation would be:

If we solve the value of x it would be:

Answer: It is 0.7

Step-by-step explanation: Seven tenths is the first digit on the right of the decimal. Hope this helped! If you need anymore help or further explanation I will be glad to help!

Answer:

-14

Step-by-step explanation:

I believe you meant 8x−y^2−3.    The expression 8x−y2−3 is meaningless.

Letting x take on the vaue -1/4 and y the value 3, we get:

8(-1/4) − (3)^2−3, or

-2        -  9 - 3, or

-2 - 12.  Final answer is -14

If the scale for the drawing is 1 inch : 4 feet , then the length of the rug in the drawing  is 2 inches  .

the actual length of the rug in the hallway is = 8 feet ;

the scale factor for the drawing is given as 1 inch : 4 feet  ;

that means 4 feet of actual length is represented by 1 inch in the drawing ,

So , 1 feet in the actual length will be = \(\frac{1}{4}\) inch in the drawing ;

that means , 8 feet of the actual length will be = \(\frac{8}{4} =2\) inch in drawing .

Therefore , the length of the rug in the drawing is 2 inches .

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Answer:

(x,y)——>(-8x, 5y)

Step-by-step explanation:

The number √7 belongs to the set of Irrational numbers. The set of irrational numbers includes numbers such as √2, √3, √5, and π, among others.

An irrational number is a real number that cannot be expressed as a fraction or a ratio of two integers. Instead, it is a non-repeating and non-terminating decimal. The square root of 7 (√7) is an example of an irrational number.

In this case, √7 cannot be simplified or expressed as a fraction because 7 does not have a perfect square root. When √7 is evaluated as a decimal, it is approximately 2.645751311... The decimal representation of √7 goes on indefinitely without repeating or terminating, making it an irrational number.

Therefore, the number √7 belongs to the set of irrational numbers.

In summary, √7 is an example of an irrational number, which is a real number that cannot be expressed as a fraction or ratio of two integers. It is a non-repeating and non-terminating decimal. The set of irrational numbers includes numbers such as √2, √3, √5, and π, among others.

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The change in the temperature is 11°.

Temperature is the physical quantity which describes, how much hot is something? Or we can say it is the quantity which measures the hotness and coldness of something. There are two main quantity values to measure the temperature which are Celsius and Fahrenheit.

Mathematically we can write :

1° Celsius = 32 Fahrenheit

Suppose if we have temperature of two difference time space then we can easily find the difference between the two by simply subtracting them.

For the given question,

last year temperature = 82 degree

temperature today = 71 degree

therefore the change in the temperature in one year is :

82 - 71 = 11 degree.

Thus , the change in temperature is 11 degree.

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Step-by-step explanation:

this is really simple : we only need to put the given x and y coordinate values into both equations and see, if both equations remain true.

(-2, -1) means x = -2, y = -1

first equation :

-1 = 3×-2 + 5 = -6 + 5 = -1

so, -1 = -1

true.

second equation :

-2 + -1 = -3

-3 = -3

true.

therefore, (-2, -1) is a solution to the linear system.

the point is the crossing point of both lines.

There will be 38 elk in the herd one year from now, rounded to a whole number.

To solve the given problem, we must use the formula for exponential growth or decay.

We'll use the following formula:

N = N0ert

Where,N is the final population;

N0 is the initial population;

r is the intrinsic growth rate;

e is the base of the natural logarithm; and

t is the time (in years).

According to the problem, the carrying capacity for a population of elk is 52, and there are currently 33 elk in the population.

The intrinsic growth rate of elk is 0.2 per year. We need to find out how many elk will be in the herd one year from now, rounded to a whole number.

Using the formula above, we can write:

N = 33e0.2 × 1= 37.98 ≈ 38

Therefore, there will be 38 elk in the herd one year from now, rounded to a whole number. Answer: 38.

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The correct answers are: c) vomiting and d) weight loss. Gastroesophageal reflux can cause frequent vomiting, which can lead to weight loss in infants.

A nurse caring for an infant with gastroesophageal reflux may observe the following findings associated with this condition:
b) wheezing
c) vomiting
d) weight loss

Infants and children diagnosed with gastroesophageal reflux should not sit or lie down immediately after a meal; patients will be advised to lie face down for at least the first hour after a meal; Sleeping in this position has been shown to reduce the frequency of gastroesophageal reflux. Expressed milk can be thickened as described, in addition to increasing the frequency of feedings; in addition, early teaching (at three (3) months) to eat rice can be attempted; small meals are also recommended; oily and spicy. foods that promote postprandial reflux by increasing gastric emptying and slowing digestion; Chocolate, mint, tomato, citrus fruits, and caffeine should be avoided, which lowers LES pressure.

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Answer:

Number of hours= 7.5

Step-by-step explanation:

Giving the following information:

The company charges a cleaning fee of $100 and an hourly rate of $45.

Her total cost for the night was $437.50

First, we need to structure the total cost formula:

Total cost= 100 + 45*x

x= number of hours

437.5= 100 + 45x

337.5/45= x

x= 7.5

Number of hours= 7.5

Answer:

Kaya rented the limo for about 7.5 hours

                  Hope this helps! good luck :)

Answer: 20

Step-by-step explanation:

where do 5 and 20 meet at the first time, 5, 10, 15, 20, so 20 would be the lcm

Answer: 20

Step-by-step explanation:

The least common multiple (LCM) for 5 and 20 will be 20. This is because if you times 5 by 4, you will get 20. Your other number is already 20 so you don't have to touch that number.

The number of pages the USB can hold is 2000000, i.e, 2×\(10^{6}\)

This question is mainly based on analyzing and then generating the balanced equation

In the question, it is given to us that one page occupies 2 KB of space

i.e, 1 page = 2kb

Let, the no. of pages occupied by the complete USB be 'n'

Also, it is given that complete space in the USB is = 4*10^6 KB

Therefore,

n×2 = 4×\(10^{6}\)

n = 2*10^6

n = 2000000 pages

So, the USB can contain 2000000 pages in it.

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f'(2) means "the slope of the tangent line to y=f(x) when x=2".

Since that tangent line is drawn, this is really asking, "What's the slope of that line?"

So, what's the rise/run for that line?

The value of f'(2) is the slope of the tangent line, which is \(\frac{1}{2}\), given by option a.

The tangent line to a function f(x) at a point \(x_0\) is given by, in point-slope form:

\(y - f(x_0) = f^{\prime}(x_0)(x - x_0)\)

That is, the slope of the line is the derivative of the function at \(x = x_0\).

\(f^{\prime}(2) = \frac{3 - 2}{2 - 0} = \frac{1}{2}\)

Given by option a.

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