Solve for x: x + 8 = 15

According to the Pythagorean theorem, The Answer is Yes the third side is greater than 1 foot.

A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

p=1 foot

b=1 foot

\(h^{2} = p ^{2} + b ^{2}\)

\(h=\sqrt {1^{2}+1^{2}}\\=\sqrt 2\\=1.41\\\)

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Answer:

Longer than 27.7 minutes.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 25, \sigma = 4\)

The slowest quarter of customers will require longer than how many minutes (to the nearest tenth) for a simple haircut?

Longer than the 100 - 25 = 75th percentile of times, which is X when Z has a pvalue of 0.75. So X when Z = 0.675. So

\(Z = \frac{X - \mu}{\sigma}\)

\(0.675 = \frac{X - 25}{4}\)

\(X - 25 = 4*0.675\)

\(X = 27.7\)

So

Longer than 27.7 minutes.

Answer:

The probability that each player will receive three picture cards = 0.0324

Step-by-step explanation:

As given,

A deck of 52 cards contains 12 picture cards

Remaining card = 52 - 12 = 40

So,

Total number of ways in which 12 picture card is distributed = \(\frac{12!}{3! 3! 3! 3!}\)

Now,

The Total number of ways in which Remaining cards are distributed = \(\frac{40!}{10! 10! 10! 10!}\)

So,

Total number of ways of getting 3 picture card and remaining card = \(\frac{12!}{3! 3! 3! 3!}\)× \(\frac{40!}{10! 10! 10! 10!}\)

= \(\frac{12! 40!}{(3!)^{4} (10!)^{4} }\)

Now,

Total number of ways to distribute 52 cards so that each people get 13 card = \(\frac{52!}{13! 13! 13! 13!} = \frac{52!}{ (13!)^{4} }\)

∴ The probability = \(\frac{\frac{12! 40!}{(3!)^{4} (10!)^{4} }}{\frac{52!}{(13!)^{4} }}\)

                            = \(\frac{12! 40!}{(3!)^{4} (10!)^{4} }\)×\(\frac{(13!)^{4} }{ 52! }\)

                           = \(\frac{12! 40!}{(3!)^{4} (10!)^{4} }\)×\(\frac{(13.12.11.10!)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41.40! }\)

                           = \(\frac{12!}{(3!)^{4} }\)×\(\frac{(13.12.11)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41}\)

                           = \(\frac{479,001,600}{(6)^{4} }\)×\(\frac{(1716)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41}\)

                           = 0.0324

∴ we get

The probability that each player will receive three picture cards = 0.0324

Answer:

(x+2)(x−10)

Step-by-step explanation:

x^2-8x-20

Factoring means  something like  this:

(x+_)(x+_)

Add together to get -8

Multiply together to get -20

think of the two numbers

Try 2 and -10:

2+-10 = -8

2*-10 = -20

Fill in the blanks of  with 2 and -10 to get

(x+_)(x+_) = (x+2)(x−10)

I hope it's right!

Answer:

Tenths

Step-by-step explanation:

The first number to the right of the decimal point is the number of tenths, the second number to the right of the decimal point is the number of hundredths, and so on.

Answer:

join the 2 equations and simplify them then use quadratic equation. easy

Answer:

Let x be the amount of the short-term note and y be the amount of the long-term note.

We know that the total amount of the two notes is $160,000:

x + y = 160,000

We also know that the total annual interest paid is $15,350:

0.11x + 0.08y = 15,350

To solve for x and y, we can use the first equation to solve for one variable in terms of the other:

y = 160,000 - x

Substitute this expression for y in the second equation:

0.11x + 0.08(160,000 - x) = 15,350

Simplify and solve for x:

0.11x + 12,800 - 0.08x = 15,350

0.03x = 2,550

x = 85,000

Substitute this value for x in the equation y = 160,000 - x to find y:

y = 160,000 - 85,000 = 75,000

Therefore, the amount of the short-term note is $85,000 and the amount of the long-term note is $75,000.

Answer:

24.6 degrees.

Step-by-step explanation:

To find the degree measure of the radians in a right triangle with hypotenuse = 7 and opposite = 3, we need to use trigonometric ratios. Since the opposite and hypotenuse are given, we can use the sine ratio.

sin(θ) = opposite/hypotenuse

sin(θ) = 3/7

Now we need to find the angle measure θ. We need to use the inverse sine or arcsine function to do this.

θ = sin^-1(3/7)

θ ≈ 0.429 radians

To find the degree measure, we must convert radians to degrees by multiplying by 180/π.

θ ≈ 0.429 x 180/π

θ ≈ 24.6 degrees

Therefore, the degree measure of the radians in the given triangle is approximately 24.6 degrees.

Answer:

3×3=9

3×8=24

3×8=24

24+24+9=57

this is the surface area

The logically equivalent statement to p → q is:

~q → ~p

The conditional statement:

p → q

Assuming p and q are propositions, the conditional statement may be expressed as:

"If p holds true, then q follows suit. "

'

Whenever p is true, q is true as well. This implies that if q is false, then p must also be false.

We can rephrase this statement cleverly using the negative propositions, which include the opposite or contradictory statements.

~p  and ~q

These mean:

Not p and Not q respectively.

Then the statement:

"If q is not true, then p is not true"

Is written as:

~q → ~p

So this is the logically equivalent statement.

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The Complete Question

Given a conditional statement p → q, which statement is logically equivalent?

~p → ~q

~q → ~p

q → p

p → ~q

Answer:

Option A. 283 cm²

Step-by-step explanation:

to find the area of the shaded sector, we use the formula:

 \(\frac{\text{angle given}}{360^\circ}\times \text{area of the circle}\)

where area of the circle = πr²

∴ for the given circle,

\(\text{Area of the sector}=\frac{\text{given angle}}{360^\circ} \times \pi r^2\)

                            =  \(\frac{100}{360}\times 3.14\times 18\times 18\)

                            = \(\frac{100}{360}\times 1017.36\)

                            = 282.6

                            ≈ 283 cm²

The approximate area of the shaded sector is 283 cm².

The given data are :

At first, make the data in order from the least to the greatest

Mean is the average of the data

Mean = (sum of the data)/(number of the data)

Sum of the data =

The number of the data = 9

So,

Median is the number which is in the middle of the data

We have 9 data

So, the median is the number (9+1)/2 = 10/2 = 5

So,

Mode is the data which is repeated more than the others

So, when we looking to the data, each number appeared one time

So,

There is no mode

The percent of the front page taken up by the prom story is 20%

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

The front page

From the front page, we have

Area front page = 5 * 4

Area front page = 20

Also, we have

Prom = 2 * 2

Prom = 4

So, we have

Percentage = 4/20 * 100%

Evaluate

Percentage = 20%

Hence, the percent of the front page taken up by the prom story is 20%

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According to the quantity theory of money, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply.Velocity can change over time, and changes in velocity may be caused by various factors.

For example, changes in velocity can be caused by shifts in payment practices, changes in the use of credit, changes in the availability of bank deposits or cash, or shifts in demand patterns.Changes in velocity may be related to changes in the money supply.

For example, if the money supply increases, the demand for money may increase, causing the velocity of money to decrease. Conversely, if the money supply decreases, the demand for money may decrease, causing the velocity of money to increase.

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Answer:

y=1/3x-2

Step-by-step explanation:

Answer: 64in cubed

Step-by-step explanation:

4x4x4

Answer:

64

Step-by-step explanation:

Volume of a cube-shaped box = a*a*a

4*4*4=64

The evaluation the city's population, to find the (average) rate of change of the population is presented as follows;

The average rate of change of the city population between 1930 and 1950 is 0.25 thousands per year

2. a. Positive

b. Negative

c. Negative

3. The population grew fastest in the decade between 1910-1920

The average rate of change of a function within an interval, is an indication of change of the function per unit change within the interval.

The city population in 1930 = 40 thousand

The population of the city in 1950 = 45 thousand

The average rate of change of the population between 1930 and 1950 therefore is;

Average rate of change = (45 - 40)/(1950 - 1930) = 0.25

The population increases at an average rate of 0.25 thousand persons per year between 1930 and 1950

2. The rate of change of the population between two years is positive, where the line joining the the two years increases from left to right and the rate of change is negative where the line decreases from left to right

a. The line joining the points 1930 and 1940 on the graph increases from left to right, therefore;

b. The location of the point on the graph in 1950 is the highest point while the location of the point on the graph corresponding to the year 1970 is lower, therefore, the line joining the points on the graph decreases from left to right and therefore;

c. 1930 corresponds to a population of 40 thousand, while 1970 corresponds to a population of 35 thousand, therefore, a line extending from 40,000 (1930) to 35,000 (1970), decreases from left to right and therefore;

3. The population growth between 1900 and 1910 is from 20 thousand to 25,000; A growth of 5 thousand

The population growth between 1910 and 1920 is from 25 thousand to 35 thousand; Representing a growth of 10 thousand

The population growth between 1920 and 1930 is from 35,000 to 40,000; A growth of 5 thousand

The change in the population between 1930 and 1940 ≈ 44,000 - 40,000 = 4,000

The change in the population between 1940 and 1950 = 45,000 - 44,000 = 1,000

Therefore, the population grew fastest between 1910 and 1920, with a growth of 10,000 in 10 years or 1,000 per year

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Answer:

The answer is "0.45385".

Step-by-step explanation:

The time is taken to reach the coast \(= \frac{\sqrt{(2^2 + x^2)}}{4}\)

The  time is taken to reach Q after reaching the coast \(= \frac{\sqrt{(1 + (3-x)^2)}}{4}\)

Total time, \(T= \frac{\sqrt{(1 + (3-x)^2)}}{4}+ \frac{\sqrt{(1 + (3-x)^2)}}{4}\)

This has to be minimum,

\(\to \frac{dt}{dx} = 0\)

\(\to \frac{\sqrt{(2^2 + x^2)}}{2} + \frac{\sqrt{1 + (3-x)^2}}{3}\\\\ \frac{x}{4}\sqrt{(4+x^2)} + \frac{(x-3)}{(4\sqrt{(x^2-6x+10)}} = 0\\\\\frac{x^2}{16} \times (4+x^2) = \frac{(x-3)^2}{16 \times (x^2-6x+10)}\\\\x^2(4+x^2) = \frac{(x-3)^2}{(x^2-6x+10)}\\\\4x^2+x^4 = \frac{ x^2+9-6x}{(x^2-6x+10)}\\\\ 4x^2+x^4(x^2-6x+10) = x^2+9-6x\\\\4x^4-24x^3+40x^2+x^6-6x^5+10x^4= x^2+9-6x\\\\x^6-6x^5+ 14x^4-24x^3+39x^2+6x-9=0\\\\\)

x=0.45385

Answer:

Step-by-step explanation:

For brand A,

Mean, x1 = (34.36 + 31.26 + 37.36 + 28.52 + 33.14 + 32.74 + 34.34 + 34.33 + 34.95)/9 = 33.44

standard deviation, s1 = √(summation(x - mean)²/n

Summation(x - mean)² = (34.36 - 33.44)^2 + (31.26 - 33.44)^2 + (37.36 - 33.44)^2 + (28.52 - 33.44)^2 + (33.14 - 33.44)^2 + (32.74 - 33.44)^2 + (34.34 - 33.44)^2 + (34.33 - 33.44)^2 + (34.95 - 33.44)^2 = 49.6338

Standard deviation = √(49.6338/9

s1 = 2.35

For brand B,

Mean, x2 = (41.08 + 38.22 + 39.59 + 38.82 + 36.24 + 37.73 + 35.03 + 39.22 + 34.13 + 34.33 + 34.98 + 29.64 + 40.60 )/13 = 36.89

Summation(x - mean)² = (41.08 - 36.89)^2 + (38.22 - 36.89)^2 + (39.59 - 36.89)^2 + (38.82 - 36.89)^2 + (36.24 - 36.89)^2 + (37.73 - 36.89)^2 + (35.03 - 36.89)^2 + (39.22 - 36.89)^2 + (34.13 - 36.89)^2 + (34.33 - 36.89)^2 + (34.98 - 36.89)^2 + (29.64 - 36.89)^2 + (40.60 - 36.89)^2 = 124.5024

Standard deviation = √(124.5024/13

s2 = 3.09

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

For a 98% confidence interval, we would determine the z score from the t distribution table because the number of samples are small.

Degree of freedom =

(n1 - 1) + (n2 - 1) = (9 - 1) + (13 - 1) = 20

z = 2.528

x1 - x2 = 33.44 - 36.89 = - 3.45

Margin of error = z√(s1²/n1 + s2²/n2) = 2.528√(2.35²/9 + 3.09²/13) = 2.935

The 98% confidence interval is

- 3.45 ± 2.935

Step-by-step explanation:

given,

base( b) = 6cm

height (h)= 11cm

now, area of parallelogram (a)= b×h

or, a = 6cm ×11cm

therefore the area of parallelogram (p) is 66cm^2.

hope it helps...

Answer:

Should be 3 units away from the picture

Step-by-step explanation:

I hope this helps! ;)

The coordinates of the image of EFG under the dilation with scale factor 3/2 and center of dilation (0, 0) are E(-3,3), F'(-3,-3) and G'(3,-3).

Dilation of a figure, means the transformation of the figure. The factor by which the given figure dilated, called the scale factor of dilation.

The image of EFG under the dilation with scale factor and center of dilation has to be drawn.

The coordinates or the triangle are E(-2,2), F(-2,-2) and G(2,-2). The new points after the dilation are,

\(E'(-2\times\dfrac{3}{2},2\times\dfrac{3}{2})=E'(-3,3)\\F'(-2\times\dfrac{3}{2},-2\times\dfrac{3}{2})=F'(-3,-3)\\G'(2\times\dfrac{3}{2},-2\times\dfrac{3}{2})=G'(3,-3)\)

The dilated image of triangle EFG is attached below.

Thus, the coordinates of the image of EFG under the dilation with scale factor 3/2 and center of dilation (0, 0) are E(-3,3), F'(-3,-3) and G'(3,-3).

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The median of the given data set is 26.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

Given the data set, we need to find the median.

So, let's arrange the numbers from smallest to largest in order to find the median.

\(\sf 15,20,22,26,28,35,36.\)

\(\text{Median}=\sf 26\)

Therefore, the median of the data set is 26.

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After 36 minutes of calls, when the function returns a line with a slope of -0.13, there will be $27.56 credit.

Mathematics deals with numbers and their variants, equations and related structures, shapes and their locations, and locations where they might be found. A function is an association between inputs and outputs where each input results in a single, unique output. A domain and a codomain, or scope, are assigned to each function. Functions are typically denoted by the letter f. (x). The input is an x. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four main categories of functions that are available.

given

Assume that the total calling time is a linear function of the credit left on a phone card (measured in dollars) (in minutes).

m(call time) + b = credit

The function produces a line with a slope of -0.14 when graphed.

After 43 minutes of calls, the card's balance is $26.02 left.

After 32 minutes of calls, there was 26.02 = -0.14(43) + b b = 26.02+6.02 b = 32.04 C(x) = -0.14x+32.04

credit?

C(32) = -0.14(32) + 32.04\sC(32) = $27.56

After 36 minutes of calls, when the function returns a line with a slope of -0.13, there will be $27.56 credit.

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Answer:

x intercept - (-2,0)

y intercept (0,5)

Step-by-step explanation:

I hope this helps!

Answer:

15. 4x¹⁰

16. 30m³

Step-by-step explanation:

15. Area of Rectangle is given by A=LW

    since W=x⁵ and L is 4 times W, L=4x⁵

    therefore, A = x⁵(4x⁵) = 4x¹⁰

16. Volume of Rectangular Prism is V=LWH

    W=6L=6m  and  H=5L=5m  and  L=m

   so V = m(6m)(5m) = 30m³