Adding 3 to some number, then multiplying the result by 7 gives 28 .
What was the original number ?

Answer:

Hat costs 4.00

T-Shirt costs 9.00

Step-by-step explanation:

Let the t-shirt be t and the hat be h

7t+h=67

5t+h=49

Equating by eliminating the h and subtracting

the two equations,

2t=18

t=9.

If t =9 in 5t + h= 49 then

5×9+h=49

45+h=49

h=4

The domain of function a(t) = \(500^t\) is  -∞ < t < ∞ and the range of the function a(t) = \(500^t\) is a(t) > 0.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given:

The function is a(t) = \(500^t\),

All real numbers fall under the expression's domain, except cases where it is undefined. In this instance, the phrase is defined even if there is no real number.

Thus, the function has no undefined points,

Domain = -∞ < t < ∞

Range = a(t) > 0 as the range of an exponential function is always positive.

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To find the median of a data set when the number of observations is odd, you follow these steps:

Arrange the data set in ascending order.

Identify the middle observation in the ordered data set.

The value of the middle observation is the median.

For example, let's say you have the following data set with an odd number of observations:

3, 5, 1, 2, 4

To find the median, you would:

Arrange the data set in ascending order: 1, 2, 3, 4, 5

Identify the middle observation, which is 3.

Therefore, the median of this data set is 3.

In summary, when the number of observations in a data set is odd, the median is the middle value when the data is arranged in ascending order.

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a) The length of AB is given as follows: 14.387.

b) The measure of angle BAC is given as follows: 78.4º.

The length of AB, from the sketch of the triangle given by the image at the end of the answer, is obtained using the law of cosines, as follows:

x² = a² + b² - 2abcos(C).

The parameters from the triangle are given as follows:

a = 8, b = 15, C = 70º.

Hence the length of AB is given as follows:

x² = 8² + 15² - 2 x 8 x 15 x cos(70º)

x² = 207

x = square root of 207

x = 14.387.

The measure of angle BAC is obtained using the law of sines, as follows:

sin(x)/15 = sin(70º)/14.387

sin(x) = 15 x sin(70º)/14.387

sin(x) = 0.9797.

x = arcsin(0.9797)

x = 78.4º.

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Answer:

\(f^{-1}\)(x)=\(\sqrt{x+3}\)  , - \(\sqrt{x+3}\)

Step-by-step explanation:

Answer: all you do is figure out what number multiplied by itself equals 100 the answer is 10. an easy way is to use the calculator and use the square root symbol

Step-by-step explanation:

The "d" format specifier is used to denote a signed decimal integer in various programming languages and formatting systems.

When used in format strings or printf-style functions, the "d" specifier indicates that the corresponding argument should be formatted as a signed decimal integer. It allows for the representation of both positive and negative whole numbers, including zero.

For example, in C programming, the printf function can be used with the "%d" format specifier to display a signed decimal integer value. Similarly, in other languages such as Python, the "{:d}" format specifier can be used with the format() function or string interpolation to represent a signed decimal integer.

Using the "d" specifier ensures that the output is formatted as a base-10 representation of a signed integer, taking into account the sign of the number.

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After an hour, the percentage of alcohol in the vat is approximately 4.92%.

After an hour of pumping beer with 6% alcohol into the vat at a rate of 5 gallons per minute and simultaneously pumping the mixture out at the same rate, the percentage of alcohol in the vat can be calculated as follows:

Initially, the vat has 500 gallons of beer with 4% alcohol content. This means there are 20 gallons of alcohol in the vat (500 * 0.04).

Now, let's consider the beer being pumped in at a rate of 5 gallons per minute with a 6% alcohol content. Over the course of an hour (60 minutes), this amounts to 300 gallons of beer, containing 18 gallons of alcohol (300 * 0.06).

As the mixture is being pumped out at the same rate, only 500 gallons of beer remain in the vat after an hour. The total alcohol in the vat is the sum of the alcohol from the initial beer and the pumped-in beer, minus the amount of alcohol pumped out. The mixture pumped out contains the same proportion of alcohol as the mixture in the vat, so it amounts to (5 gallons/minute * 60 minutes) * X%, where X% is the percentage of alcohol in the mixture at the end of an hour.

To find X%, we can set up the following equation:

20 (initial alcohol) + 18 (alcohol pumped in) - 5 * 60 * X% = 500 * X%

Solving for X, we get:

38 - 300 * X% = 500 * X%

Rearranging and solving for X, we find that:

X% ≈ 4.92%

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The answer of the function found to be x = −4 and x = 2,  with M = 38.

We must consider the function,

f (x) = x³ + 6x² + 6

Over the interval  

-5 \(\leq\) x \(\leq\) 2

To obtain the extrema we start from the function's derivative.

f' (x) = 3x² + 12x

Equating it to 0,

f' (x) = 0 = 3x(x +4) = 0

We arrive at two solutions,

x1 = 0,     x2 = -4   both inside the interval.

Evaluating the function at the stationary points,

f (x1) = 6

f (x2) = (-4)³ + 6 . (-4)² + 6 = -64 + 96 + 6 = 38

These values must be compared to that of the function at the interval frontiers,

f (-5) = (-5)³ + 6 . (-5)² + 6 = -125 + 150 + 6 = 31

f (2) = 2³ + 6 . 2² + 6 = 38

Comparing the results we can conclude that the function attains its absolute minimum at,

x = 0,      m = 6

Meanwhile, the absolute maximum is attained at the points,

x = −4 and x = 2,  with M = 38.

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To express the integrand as a rational function, we can make the substitution u = 1 + x^2. Then, du/dx = 2x, so dx = du/(2x).

You are asked to evaluate the integral of a function that can be expressed as a rational function using substitution. The given integrand is:

∫((Tc-4)^(-1/3) dTc)

Step 1: Make a substitution to express the integrand as a rational function
Let's perform a substitution:
u = Tc - 4

Then, differentiate both sides with respect to Tc:
du/dTc = d(Tc - 4)/dTc = 1

Now, solve for dTc:
dTc = du

Now, substitute the expressions for u and dTc into the original integrand:
∫(u^(-1/3) du)

Step 2: Evaluate the integral
Now, integrate the new expression:
∫(u^(-1/3) du) = (3/2)u^(2/3) + C

Step 3: Substitute back to the original variable, Tc
Now, substitute back the original variable, Tc, using u = Tc - 4:
(3/2)(Tc - 4)^(2/3) + C

Therefore, the integral of the given expression is:
(3/2)(Tc - 4)^(2/3) + C

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The samples in the first proposal are independent, while the samples in the second proposal are dependent.

In the first proposal, where the manufacturer randomly samples 10 different dealerships for each set of sales numbers (last year and 15 years ago), the samples are independent. This is because the selection of dealerships for one set of sales numbers does not affect or influence the selection of dealerships for the other set of sales numbers. Each dealership is chosen randomly and independently for each set.

On the other hand, in the second proposal, where the manufacturer randomly samples 10 dealerships for both sets of sales numbers, the samples are dependent. This is because the selection of dealerships for one set of sales numbers is directly tied to the selection of dealerships for the other set of sales numbers. The same 10 dealerships are chosen for both sets, so the samples are not independent.

The choice between independent and dependent samples can have implications for statistical analysis. Independent samples allow for direct comparisons between the two sets of sales numbers, while dependent samples may introduce potential bias or confounding factors due to the shared dealership selection.

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Answer:

Step-by-step explanation:

TU=8

WU=10

TX=5

TV=10

I THINK

Answer:

DOC = 70

BOC = 110

AOD = 110

Step-by-step explanation:

AOB is supplementary to BOC and AOD, which means together they equal 180. 180-70=110, so BOC and AOD are both 110.

AOB and DOC are vertical angles to each other, so are AOD and BOC. Vertical angles are always equal to each other. So since AOB is 70, so is DOC.

Hope this makes sense:)

Answer:

Is 50

Step-by-step explanation:

I don’t know

The confidence multiplier z* for constructing a 97% confidence interval is z* = 2.33

To compute the value of the confidence multiplier z* for constructing a 97% confidence interval, we can use the standard normal distribution table (also known as the z-table). The formula for computing the confidence interval for a population mean (μ) is given by:CI =x ± z*(σ/√n)

Where:x is the sample mean σ is the population standard deviation

n is the sample size

z* is the confidence multiplier

We can use the following steps to calculate z* for a 97% confidence interval:

1: Find the area of the middle region

To find the area of the middle region, we subtract the confidence level from 100% and divide the result by 2. In this case, the confidence level is 97%, so the area of the middle region is:Area of middle region = (100% - 97%) / 2 = 1.5%

2: Find the area to the right of the middle region

To find the area to the right of the middle region, we add the area of the middle region to 50%.

In this case, the area to the right of the middle region is:

Area to the right = 50% + 1.5% = 51.5%

3: Look up the z-score in the z-tableWe can use the z-table to find the z-score that corresponds to an area of 51.5% to the right of the mean.

The closest value we can find is 0.01, which has a z-score of 2.33.

Therefore, the confidence multiplier z* for constructing a 97% confidence interval is z* = 2.33 (rounded to two decimal places).

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Answer:

Step-by-step explanation:

The only way this can be factored is by pulling out the GCF. 2 and x are common to both terms:

\(2x(x^2-100)\)

BUT you should also recognize that what's inside the parenthesis is the difference of perfect squares. And that factors to

(x - 10)(x + 10). So the complete factorization is

2x(x - 10)(x + 10)

Volume of the cylinder as we know is πr²h, using the volume formula is = 1085.18ft³.

A cylinder's capacity, which indicates how much material it can carry, is determined by its volume. Geometry provides a precise formula for determining a cylinder's volume, which may be used to determine how much of any material, liquid or solid, can fit inside of it equally.

A cylinder is a three-dimensional object having two parallel, identical congruent bases.

In the given figure,

Radius of cylinder = 6ft.

Height of cylinder = 9.6ft.

Volume of cylinder = πr²h

= 3.14 × 6² × 9.6

= 1085.18ft³

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how do u not know this

Step-by-step explanation:

my guy

Answer:

C. 7.50 hrs

Step-by-step explanation:

Since it takes 90 mins to clean 11 windows, the rate that it takes the washer per window is \(\frac{90}{11}\) minutes. At this rate, if he were to clean 55 windows it would take him \(\frac{90}{11}(55) = 450\) minutes. This translates into 7.50 hrs.

Answer:

(5x+1)(x+4)

Step-by-step explanation:

5*4 = 20

20*1 = 20 and 20+1 = 20

5x^2+20x+1x+4

5x(x+4)1(x+4)

5x+1)(x+4

The probability of getting exactly 2 tails in 7 flips of a coin with a probability of tails being 3/4 is 189/16384 or approximately 0.0115.

We can use the binomial distribution formula to solve this problem. Let X be the number of tails that come up in 7 flips of the coin. Then X follows a binomial distribution with n = 7 and p = 3/4 (since the probability of tails is 3/4).

The probability of getting exactly 2 tails is given by:

P(X = 2) = (7 choose 2) * (3/4)^2 * (1/4)^5

= (21 * 9/16 * 1/1024)

= 189/16384

So the probability that George flips exactly 2 tails is 189/16384, or approximately 0.0115.

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Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The distance between two points in a plane is the length of the line segment connecting them. The formula d=((x2 - x1)2 + (y2 - y1)2) is frequently used to determine the separation between two points.

The length of the line segment bridging two locations in a plane is known as the distance between them. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points. This equation can be used to determine the separation between any two locations on an x-y plane or coordinate plane.

The length of the line segment is the distance between two points. Congruent segments are those that share the same length. By using a ruler to draw a line, we may determine how far apart two points are.

x,y = (-8,0) (-8,0)

or

x/y = -8/0

If there was an association between L and K, we would use x,y = 8,0.

Since the query reads "between point K and point L," the x,y relationship becomes "-8,0."

Therefore, the answer is -8,0.

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To compare the greater pay between a salary of $74,000 per year and an hourly rate of $40 for 80 hours every fortnight, we need to calculate the total earnings for each option.

Salary per year:

To calculate the total earnings for the salary option, we simply take the annual salary of $74,000.

Total earnings = $74,000 per year

Hourly rate:

To calculate the total earnings for the hourly rate option, we need to determine the total number of hours worked in a year. Since there are 26 fortnights in a year, and the lawyer works 80 hours per fortnight, the total number of hours worked in a year would be:

Total hours worked per year = 26 fortnights * 80 hours/fortnight = 2,080 hours

Now we can calculate the total earnings:

Total earnings = Hourly rate * Total hours worked per year

= $40/hour * 2,080 hours

= $83,200

Comparing the two options, we find that the greater pay is $83,200 from the hourly rate, which exceeds the $74,000 salary per year.

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The figure is being rotated.

If an object is being reflected, the object is flipped across a line without changing its size and shape. The line is called the line of reflection. It follows a mirror image like this:

If an object is being translated, the object is being moved to any direction without changing its size, shape, or orientation.

When an object is being rotated, it is rotated around a fixed point without changing its size or shape.

Since the figure that we have is neither a translation and a reflection, we have a rotation right here. The figure is being rotated 180 degrees.

Answer:

£616

Step-by-step explanation:

700 - 12% = 616

616 is 12% less than 700

Answer:

6 runners

Step-by-step explanation:

Complete question

A relay race covers 1 1/2 kilometers, and each runner on a team will run 1/4 of a kilometer.  How many runners are needed for a team?

Given that;

1 runner = 1/4 km

If a relay race covers  1 1/2 km, hence;

x runner = 1 1/2 km

Divide both expressions

1/x = (1/4)÷(1 1/2)

1/x = 1/4 ÷ 3/2

1/x = 1/4 * 2/3

1/x = 2/12

Cross multiply

2x = 12

x = 12/2

x = 6

Hence 6 runners are needed for the race

Answer: b. 6

Step-by-step explanation: