Set up and solve an equation to find the
measure of each missing angle.
B
63
A
(2x+8)
C
(x + 7)°

Answer:

R = 1.2%

Step-by-step explanation:

Given the following data;

Principal = 425

Time = 2

Simple interest = 10.20

To find the annual interest rate;

Mathematically, simple interest is calculated using this formula;

\( S.I = \frac {PRT}{100} \)

Where;

Substituting into the equation, we have;

\( 10.20 = \frac {425*R*2}{100} \)

\( 10.20 = \frac {850R}{100} \)

Cross-multiplying, we have;

\( 1020 = 850R \)

\( R = \frac {1020}{850} \)

R = 1.2%

Therefore, the annual interest rate is 1.2 percent.

Answer:

.988  or 98.8%

Step-by-step explanation:

The probability that the technical problem is solved can be defined as follows:

The probability that P solves the problem or probability that Q solves the problem or probability that both (P and Q) solve the problem

The probability that P solves the problem = 1/2

The probability that Q solves the problem= 1/4

The probability that both solve the problem = (1/2) x (1/4) = 1/8

The probability that the technical problem is solved =

The correct option is C

The calculated volume of the prism is 702 cubic cm

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

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

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Answer:

2/3 or 67%

Step-by-step explanation:

To find the exact probability for you to reach into the orange balls you'll have to do a data table on which you'll include how many orange balls are by the total amount of balls that are within the urn.

For example:
The urn contains:

* 10 red balls
* 20 yellow balls
* 60 orange balls

Total amount of balls that you have on the urn is 90, you'll get this result by doing a simple addition of the table of content.

Afterwards, we have to find the probability, so you will have to take the amount of orange balls (which is 60) and divide it by 90 (Which is the total amount of balls you have on the urn).

60/90

A quick tip for you to do this on a simplified manner is by dividing the numerator and the denominator by their greatest common divisor (Which in this case is 30) (30x2 = 60) (30x3 = 90)

60/90 = (60 divided 30) / (90 divided 30) = 2/3

To resolve this problem, we get that the probability of selecting an orange ball is 2/3 or approximately 0.67 which we'll simplify to 67%

I hope this helped you

Answer:

Margin of Error concept & example

Step-by-step explanation:

Margin of Error refers to range of values around sample statistic, within confidence interval. It denotes, expected percentage points of difference from real population value.

Example : With 95% Confidence Interval with (lets say 4) percent Margin of Error implies that - statistic is expected to be within 4% deviation around population mean 95% of the time.

It applies to pie case also. People liking chocolate pie are likely to be within ME% around sample percentage, with probability of CI% .

Answer:

tourist: 28%

non-tourist: 72%

Step-by-step explanation:

total: 50

tourists: 14

non-tourists:50 - 14 = 36

tourist percentage: 14/50 × 100% = 28%

non-tourist percentage: 36/50 × 100 = 72%

we know that

In any triangle the sum of the interior angles must be equal to 180 degrees

so

In the first triangle (bottom) we have

64+71+x=180

Solve for x

x is the missing angle

135+x=180

x=180-135

x=45 degrees

The first missing angle is 45 degrees

step 2

triangle of the top

we know that

The first missing angle is 64 degrees by vertical angles

so

we have that

64+56+y=180

solve for y

120+y=180

y=180-120

y=60 degrees

Answer:

\(x=38\)

Step-by-step explanation:

\(We\ are\ given\ that,\\\angle KLO=134\\\angle OMN= 84\\Hence\ we\ observe\ that,\\\angle KLO\ and\ \angle OLM\ form\ a\ linear\ pair\ and\ hence,\ are\ supplementary.\\Hence,\\\angle KLO\ + \angle OLM=180\\Substituting\ \angle KLO=134,\\134+\angle OLM=180\\\angle OLM=180-134\\\angle OLM=46\\Similarly,\)

\(\angle OMN\ and\ \angle OML\ form\ a\ linear\ pair\ and\ hence,\ are\ supplementary.\\Hence,\\\angle OMN\ + \angle OML=180\\Substituting\ \angle OMN=84,\\84+\angle OLM=180\\\angle OLM=180-84\\\angle OLM=96\\\)

\(Now\ lets\ consider\ \triangle OML,\\\angle OLM + \angle OML+ \angle LOM=180 [Angle\ Sum\ Property\ Of\ a\ triangle]\\Hence\ substituting\ \angle OLM=46, \angle OML=96, \angle LOM=x\\46+96+x=180\\142+x=180\\x=180-142\\x=38\)

Answer:

a)Parametric equations are

X= -10t

Y= -10t and

z= 25+25t

b) Symmetric equations are

(x/-10) = (y/-10) = (z- 25)/25

Step-by-step explanation:

We were told to fin two things here which are ; a) the parametric equations and b) the symmetric equations

The given two points are (0, 0, 25)and (10, 10, 0)

The direction vector from the points (0, 0, 25) and (10, 10, 0)

(a,b,c) =( 0 -10 , 0-10 ,25-0)

= < -10 , -10 ,25>

The direction vector is

(a,b,c) = < -10 , -10 ,25>

The parametric equations passing through the point (X₁,Y₁,Z₁)and parallel to the direction vector (a,b,c) are X= x₁+ at ,y=y₁+by ,z=z₁+ct

Substitute (X₁ ,Y₁ ,Z₁)= (0, 0, 25), and (a,b,c) = < -10 , -10 ,25>

and in parametric equations.

Parametric equations are X= 0-10t

Y= 0-10t and z= 25+25t

Therefore, the Parametric equations are

X= -10t

Y= -10t and

z= 25+25t

b) Symmetric equations:

If the direction numbers image and image are all non zero, then eliminate the parameter image to obtain symmetric equations of the line.

(x-x₁)/a = (y-y₁)/b = (z-z₁)/c

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:

Exercise Problem Solution

1 Find the perimeter of a triangle the sides of which are 10 in, 14 in and 15 in. P = 10 in + 14 in + 15 in = 39 in

2 A rectangle has a length of 12 cm and a width of 4 cm. Find its perimeter. P = 12 cm + 12 cm + 4 cm + 4 cm = 32 cm

3 Find the perimeter of a regular hexagon with each side measuring 8 m. P = 6(8 m) = 48 m

4 The perimeter of a square is 20 ft. How long is one side? 20 ft ÷ 4 = 5 ft

5 The perimeter of a regular pentagon is 100 cm. How long is one side? 100 cm ÷ 5 = 20 cm

Step-by-step explanation:

Answer:

61 square feet

Step-by-step explanation:

Your rectangle has a area of A = w l

A = 4*10 = 40

The triangle has a area of A = h (b/2)

A = 7 (6/2)

A = 21

Add both for the area

Answer:

dimes- 8

nickels- 4

Step-by-step explanation:

dime=10 cents

nickels=5 cents

5 x 4 = 20

10 x 8 = 80

80 + 20 = 100

... please give brainliest ...

The value of standard deviation 's' is 2.08700, as indicated in the display.

Standard deviation is a measurement of how evenly distributed a set of numbers is. Since the variance is the average of the squared deviations from the mean, it is the square root of the variance.

The value of s is 2.08700, as indicated in the display.

The symbol "Sx" represents the sample standard deviation, which is commonly denoted as "s". The other values in the display are:

So, the correct answer is 2.08700.

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Answer:

490000

Step-by-step explanation:

Substituting \(x=40\),

\(I=-425(40)^2 + 45500(40) - 650000=490000\)

Answer:

x = 65.26 degrees or x = 245.26 degrees.

Step-by-step explanation:

To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:

4tan(x) = 7

Then, we can divide both sides by 4 to get:

tan(x) = 7/4

Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:

x = tan^-1(7/4)

Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).

However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).

To find the solution in the first quadrant, we can simply use the value we just calculated:

x = 65.26 degrees (rounded to two decimal places)

To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:

x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)

So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:

x = 65.26 degrees or x = 245.26 degrees.

Answer:

Purchases made with this card are withdrawn directly from a bank account.

D

I think I think i think I think

The standard deviation of the response time is 1.53 minutes.

To get standard deviation, we will determine z-scores corresponding to the given percentiles and use them to calculate the standard deviation.

Z-score = z = (x - μ) / σ

For the lower bound of 10 minutes:

z = (10 - 13) / σ

For the upper bound of 16 minutes:

z = (16 - 13) / σ

As normal distribution is symmetric, the z-score corresponding to the lower tail of 2.5% is -1.96, and the z-score corresponding to the upper tail of 2.5% is 1.96.

Using z-scores, we set up  equations:

(10 - 13) / σ = -1.96

(16 - 13) / σ = 1.96

Solving the first equation:

-3 / σ = -1.96

σ = -3 / -1.96

Solving the second equation:

3 / σ = 1.96

σ = 3 / 1.96

Dividing both sides by 1.96:

-3 / 1.96 = σ

1.53 = σ

Full question:

The respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes. What is S.D. of the response time.

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Answer:

(a) The probability of a woman receiving a salary in excess of $75,000 is 0.1271.

(b) The probability of a man receiving a salary in excess of $75,000 is 0.0870.

(c) The probability of a woman receiving a salary below $50,000 is 0.9925.

(d) A woman would have to make a higher salary of $81,810 than 99% of her male counterparts.

Step-by-step explanation:

Let the random variable X represent the salary for women and Y represent the salary for men.

It is provided that:

\(X\sim N(67000, 7000^{2})\\\\Y\sim N(65500, 7000^{2})\)

(a)

Compute the probability of a woman receiving a salary in excess of $75,000 as follows:

\(P(X>75000)=P(\frac{X-\mu_{x}}{\sigma_{x}}>\frac{75000-67000}{7000})\)

                     \(=P(Z>1.14)\\\\=1-P(Z<1.14)\\\\=1-0.87286\\\\=0.12714\\\\\approx 0.1271\)

Thus, the probability of a woman receiving a salary in excess of $75,000 is 0.1271.

(b)

Compute the probability of a man receiving a salary in excess of $75,000 as follows:

\(P(Y>75000)=P(\frac{Y-\mu_{y}}{\sigma_{y}}>\frac{75000-65500}{7000})\)

                     \(=P(Z>1.36)\\\\=1-P(Z<1.36)\\\\=1-0.91309\\\\=0.08691\\\\\approx 0.0870\)

Thus, the probability of a man receiving a salary in excess of $75,000 is 0.0870.

(c)

Compute the probability of a woman receiving a salary below $50,000 as follows:

\(P(X<50000)=P(\frac{X-\mu_{x}}{\sigma_{x}}<\frac{50000-67000}{7000})\)

                     \(=P(Z>-2.43)\\\\=P(Z<2.43)\\\\=0.99245\\\\\approx 0.9925\)

Thus, the probability of a woman receiving a salary below $50,000 is 0.9925.

(d)

Let a represent the salary a woman have to make to have a higher salary than 99% of her male counterparts.

Then,

   \(P(Y\leq a)=0.99\)

\(\Rightarrow P(Z<z)=0.99\)

The z-score for this probability is:

z-score = 2.33

Compute the value of a as follows:

\(\frac{a-\mu_{y}}{\sigma_{y}}=2.33\\\\\)

    \(a=\mu_{y}+(2.33\times \sigma_{y})\\\\\)

       \(=65500+(2.33\times7000)\\\\=65500+16310\\\\=81810\)

Thus, a woman would have to make a higher salary of $81,810 than 99% of her male counterparts.

Answer:

Choice B is the closest

Step-by-step explanation:

A-lateral = 2πrh

r = D/2 = 16.5/2 = 8.25

h = 14

A = 2π(8.25)(14) = 725.7 in²

Answer:

5.25 kilometers

Step-by-step explanation:

63k/60 = 1.05k

1.05k x 5 = 5.25k

The inverse of the equation is determined as \(y = \log_{6}(-3x)\).

option D is the correct answer.

The inverse of the equation is calculated by applying the following method;

The given equation;

y = - 6ˣ/3

The inverse of the equation is calculated as;

multiply through by 3

\(-3x = 6^y\)

Take the logarithm of both sides of the equation with base -6:

\(\log_{6}(-3x) = y\)

Finally, replace y with x to obtain the inverse equation as follows;

\(y = \log_{6}(-3x)\)

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Answer:

A ratio can be expressed as a word description, with a colon or as a fraction.

Step-by-step explanation:

A ratio can be expressed as a word description, with a colon or as a fraction.

Quantitatively, a ratio is a number representing a comparison between two named values. It is the relative magnitude of two quantities usually expressed as a quotient.

Thus, a ratio can be expressed as a word description between two quantities, for example:

four to five.

It can be represented with a colon. i.e  4:5

Or as a fraction i.e. \(\dfrac{4}{5}\)

Answer:

A) \(x=-1\pm\sqrt{\frac{13}{6}}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}\)

Answer:

The LCL for a 90% confidence interval for p is 0.82.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

A lawn service owner is testing new weed killers. He discovered that a particular weed killer was effective 89% of time. Suppose that this estimate was based on a random sample of 60 applications.

This means that \(\pi = 0.89, n = 60\)

90% confidence level

So \(\alpha = 0.1\), z is the value of Z that has a pvalue of \(1 - \frac{0.1}{2} = 0.95\), so \(Z = 1.645\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.89 - 1.645\sqrt{\frac{0.89*0.11}{60}} = 0.8236\)

Rounding to two decimal places, the LCL for a 90% confidence interval for p is 0.82.

The three consecutive multiples of 3 are 15, 18 and 21

First, let's determine three successive multiples of 3:

The subsequent two would be "x+3" and "x+6" if we call the initial number "x".

Since we are aware that the third number (x+6) is one more than the first two numbers (x + x+3), we can write the following equation:

2/3(x + x+3) = (x+6) + 1

Simplifying this equation, we get:

2/3(2x+3) = x+7

Multiplying both sides by 3, we get:

2(2x+3) = 3(x+7)

Expanding and simplifying, we get:

4x + 6 = 3x + 21

Subtracting 3x and 6 from both sides, we get:

x = 15

Therefore, the three consecutive multiples of 3 are 15, 18 and 21

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Combining like terms yields 7x⁵ - x³ - x² + 4x.

Acceleration is the rate of change of velocity over time

His final velocity is 14.4 meters per second

From the question, we have:

Using the first equation of motion, we have:

\(v = u + at\)

So, the equation becomes

\(v = 0 + 1.8 * 8\)

\(v =14.4\)

Hence, the final velocity is 14.4 meters per second

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The maximum height reached by the fireball is 25 feet.

What is function ?

Function can be defined in which it relates an input to output.

The height h of a fireball launched from a Roman candle with an initial velocity of v feet per second is given by the equation h(t) = −16t*t+ vt, where t is time in seconds after launch

We can see from the graph that the height of the fireball is 0 when t = 0, which means the fireball was launched from the ground. At this point, the graph intersects the y-axis at the point (0,0). From the equation, we know that the initial velocity v is the coefficient of t, which means that v = 40 feet per second.

What is the maximum height reached by the fireball?

The maximum height reached by the fireball corresponds to the highest point on the graph. We can see from the graph that this occurs at approximately t = 1.25 seconds. To find the maximum height, we need to find the value of h at this time. We can substitute t = 1.25 into the equation to get:

h(1.25) = −16(1.25)*(1.25) + 40(1.25) = 25 feet

Therefore, the maximum height reached by the fireball is 25 feet.

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