In the right-angled triangle ABC, cos C = 4/5 and BC = 16 cm, find the following:

i) AC
ii) AB​

Among dog owners, 40% also keep cats.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured

According to our question-

27% of households only own dogs.

12 percent own a cat but no dog.

18% of people own both dogs and cats.

43% don't own either a dog or a cat.

18/45 dog owners also have cats.

*100% = 40%

Among dog owners, 40% also keep cats.

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Probability that a card is chosen is not blue is 3/5

Probability means possibility.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty.topic. One is the probability of every event in a sample space.

According to the probability formula, the likelihood that an event will occur is equal to the proportion of favorable outcomes to all outcomes.

probability that an event will occur P(E) = Number of favorable outcomes/Total Number of outcomes

Total number of cards in the box is 5+8+7=20 cards

Number of cards that are not not blue = 5 + 7 = 12 cards

Probability that a card is chosen is not blue = Number of favorable outcomes/Total Number of outcomes = 12/20 = 3/5

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Probability that a card is chosen is not blue is 3/5

What is Probability?

Probability means possibility. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. topic. One is the probability of every event in a sample space.

According to the probability formula, the likelihood that an event will occur is equal to the proportion of favourable outcomes to all outcomes.
probability that an event will occur P(E) = Number of favorable outcomes/Total Number of outcomes
Total number of cards in the box is 5+8+7=20 cards
Number of cards that are not not blue = 5 + 7 = 12 cards
Probability that a card is chosen is not blue = Number of favorable outcomes/Total Number of outcomes = 12/20 = 3/5

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If the diameter of a small red beachball is 8 inches, then the cone with the same radius and a height of a 8 inches would fit into the beachball 1/2 times and the volume of the cone would be about 536 in^3.

Explanation :

If the diameter of a small red beachball is 8 inches, then the cone with the same radius and a height of a 8 inches would fit into the beachball 1/2 times, because Centre radius will reduced to point when it reaches its full height.

The volume of the cone would be about 536 in^3.

Volume of a cone = 1/3 π [tex]r^{2}[/tex] *h

                              = 1/3 x π x [tex]8^{2}[/tex] x 8 = 536

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Answer:

Step-by-step explanation:

You want to know how many times the volume of a cone 8 inches in diameter and 8 inches high will fit into the volume of a beachball that is 8 inches in diameter, and you want the approximate volume of the cone.

The equation for the volume of a sphere based on its diameter is ...

  V = π/6d³

The equation for the volume of a cone is usually written ...

  V = 1/3πr²h

For the cone in this problem, with both diameter and height equal to that of the sphere, we can rewrite the volume equation as ...

  V = 1/3π(d/2)²·d = π/12d³ . . . . . . where d=8 inches, the sphere diameter

Then the ratio of the sphere's volume to that of the cone is ...

  Vs/Vc = ((π/6)d³)/((π/12)d³) = 12/6 = 2

The volume of the cone will fit into the volume of the sphere two (2) times.

The volume of the cone is ...

  V = (π/12)8³ = 128π/3 ≈ 134 . . . . cubic inches

The cone's volume is about 134 in³.

__

Additional comment

Note that we have taken the wording "with the same radius" to mean that the radius of the cone is the same as the radius of the sphere.

Alternatively, it could mean the radius of the cone is the same as the dimension given for the diameter of the sphere. In that case, the volume of the cone is 4 times as great, so its volume of 536 in^3 will fit into the sphere 1/2 times.

Answer:

Answer:

B.  110°

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Linear Pair

Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).

Corresponding Angles Postulate

When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.

Given:

Apply the Vertical Angle Theorem to find the measure of angle 8:

⇒  m∠3 = m∠8 = 70°

As angles 7 and 8 form a linear pair:

⇒  m∠7 + m∠8 = 180°

⇒  m∠7 + 70° = 180°

⇒  m∠7 = 110°

As line p is parallel to line q, apply the Corresponding Angles Postulate to find the measure of angle 15:

⇒  m∠15 = m∠7 = 110°

Therefore, the measure of angle 15 is 110°.

Answer:

10/7 or 1 3/7

Step-by-step explanation:

1. change from mixed fraction to improper fraction, 5/2 and 7/4

2. instead of the dividing the fractions as is, multiply the reciprocal which would be 5/2 multiplied by 4/7. Then you cross multiply. 2 into 2, 1 and 2 into 4, 2. So now you're left with 5 and 2/7 since 5/1 is basically 1.

3. simplify to just 10/7

Answer:

10/7 or 1 3/7

I took a test with that question.

Yes, by definition cotx=1tanx, and tanx=sinxcosx, so cotx=1sinx/cosx=cosxsinx.

[tex]osx2=cos(x2)=cos(x[/tex]×[tex]x) while cos2(x)=cos(x)[/tex]×[tex]cos(x)=(cos(x))2.[/tex]

[tex]cos^2xcot^2+cos^2x\\= cos^2x(cot^2x+1)\\= cos^2x csc^2x\\= cot^2x < ==Answer[/tex]

[tex]cos2x = 1 - 2 sin 2x.\\cos2x = (1 - tan 2x) / (1 + tan2x)[/tex]

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A series that is neither mathematical nor geometric is described by the provided sequence. Which is the proper response would be a choice (B).

A grouping of numbers in a specific order is known as an arithmetic sequence.

The following question gives the sequence as follows: 1, 6, 7, 13,...

We must determine the kind of the current sequence.

According to the question, we have 1, 6, 7, 13,...

For verification as an arithmetic series:

The usual deviation between 1 and 6 is given by d = 6 - 1 = 5.

Commonly, 6 and 7 differ by 1 when d = 7 - 6

It is not an arithmetic sequence since the common difference between subsequent terms is not the same.

In order to verify it as a geometric sequence:

r = 6/1 = 6 is a common ratio between 1 and 6.

r = 7/6 is a common ratio between 6 and 7.

It is not a geometric sequence since the common ratio between subsequent terms is not the same.

A series that is neither mathematical nor geometric is described by the provided sequence.

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Answer:

(f +g)(x)=7x²+x-4

Step by step:

first you have to add both f(x) and g(x) to find (f +g)(x)

Answer:

Step-by-step explanation:

A

The point of intersection between the function f(x) and g(x) is x = 4 then, g(x)=18 where option E (4,18) is correct answer.

What is a function?

A function is defined as a relation between a set of inputs having one output each.

We have,

f(x) = ( x + 5 ) ( x - 2 )

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

To find the points of intersection between the two functions we must equal the function.

f(x) = g(x)

( x + 5 ) ( x - 2 ) = ( 2x + 1 ) ( x - 2 )

( x - 2 ) gets canceled

x + 5 = 2x + 1

5 - 1 = 2x - x

4 = x

x = 4

This means that at x =4 the function f(x) and g(x) intersect.

we can see that at x = 4 both the functions have the same value.

f(x) = ( x + 5 ) ( x - 2 ) = ( 4 + 5 ) ( 4 - 2 ) = 9 x 2

f(x) = 18

g(x) = ( 2x + 1 ) ( x - 2 ) = ( 2 x 4 + 1 ) ( 4 - 2 ) = ( 8 + 1 ) ( 4 - 2 )

     = 9 x 2

g(x) = 18

Thus the point of intersection between the function f(x) and g(x) is x = 4 then, g(x) =18 where option E (4,18) is correct answer.

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Answer:

880 is the answer

Step-by-step explanation:

hope this helps

The expression which defines the nth term of the given sequence, in terms of n as required in the task content is; T (n) = 1 + 7(n - 1).

It follows from the task content that the expression which represents the nth term of the given sequence be determined.

By observation, the first term, a of the sequence is; 1.

Also, since; 8 - 1 = 15 - 8 = 22 - 15 = 29 - 22 = Common difference, d = 7.

It follows that the expression is a arithmetic sequence which can be modelled by;

T (n) = a + d (n - 1)

Since the constant common difference of consecutive terms in the sequence is; 7,

The required expression for the nth term of the expression is;

nth = 1 + 7(n -1)

On this note, the nth term is given by the expression; T (n) = 1 + 7 (n -1).

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By converting the given improper fraction 910/238 as a mixed number we get the result as 3[tex]\frac{14}{17}[/tex].

A mixed number is one that includes both a whole number and a legal fraction. A number with both an integer (whole number) and a correct fraction is referred to as a mixed number or mixed fraction (a fraction whose numerator is less than its denominator).

Pretzels, peanuts, Cheerios, and of course rice and corn Chex make up this mixture, which is dubbed a "mix." Numerals with both an integer and a fraction included are known as mixed numerals. The term "mixed number" refers to the combination of these two types of numbers.

Given,

910/238 is an improper fraction.

Now by dividing both the numerator and denominator by 14, we get

(910/14)/(238/14)

=65/17

Now, 65/17 can be written as a mixed number as 3[tex]\frac{14}{17}[/tex].

Therefore, By converting the given improper fraction 910/238 as a mixed number we get the result as 3[tex]\frac{14}{17}[/tex].

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The complete question is:

"Find 910/238. Express your answer as a mixed number in simplest form."

The interval of true average price of a regular room with a king size bed in the resort community with 99% confidence is ( 14.74, 48.89 ).

One method of determining the actual population mean is by using a confidence interval for the mean. A confidence interval provides a lower estimate and an upper estimate rather than just the mean.

A confidence interval expresses the degree of uncertainty surrounding a given statistic. A margin of error is frequently used with confidence intervals. It reveals the degree to which you may be certain that the findings of a poll or survey correspond to what you would anticipate discovering if it were possible to poll the complete population. Levels of confidence are inextricably linked to confidence intervals.

x = mean;

99% confidence interval for μ is

(x - t * S) /√n  <  μ <( x + t * S) /√n;

(135 - 2.898 * 25 )/√18 < μ < (135 + 2.898 * 25)/√18;

14.74<  μ< 48.89;

99% CI is ( 14.74, 48.89 ) ;

critical value at 0.01 significance level with 17 df = 2.898

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The total surface area of the solid object is the sum of the surface area of the cylinder and the surface area of the cone.

The surface area of the cylinder is 2πr(r+h), where r is the radius of the cylinder and h is its height.

The surface area of the cone is πr(l+r), where r is the radius of the cone and l is its slant height.

Since the cylinder and the cone have the same radius, we can call this radius r.

The total surface area of the solid object is therefore 2πr(r+h) + πr(l+r).

We are told that this total surface area is equal to 6336/210 = 30 sq. cm.

Thus, we can set up the equation: 2πr(r+h) + πr(l+r) = 30.

We are trying to find the value of l, which is the slant height of the cone. We are given the value of h, which is the height of the cylinder. We can substitute this value into the equation to get:

2πr(r+30) + πr(l+r) = 30.

This equation can be rearranged and solved for l to find the slant height of the cone.

l = sqrt(900 - 60r).

Since we are given that the slant height of the cone is 26 cm, we can substitute this value into the equation to solve for the radius of the cone:

26 = sqrt(900 - 60r)

Solving for r, we find that the radius of the cone is 15 cm.

Substituting this value back into the equation for the slant height of the cone, we find that the height of the cone is:

l = sqrt(900 - 60(15)) = sqrt(300) = 17.67 cm.

Thus, the height of the cone is approximately 17.67 cm.

By using slope intercept form of equation of line, the graph of

h(x) = [tex]-\frac{2}{5}x + 4[/tex] has been shown

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Let the independent variable be x and dependent variable be h(x)

The dependent variable decreases 2 units for every 5 units the independent variable increase.

Slope = [tex]-\frac{2}{5}[/tex]

So,

h(x) = [tex]-\frac{2}{5}x + c[/tex]

Now,

h(0) = 4

So, c = 4

h(x) = [tex]-\frac{2}{5}x + 4[/tex]

The graph has been attached here-

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The  level of confidence as a would accompany each of the given intervals are a. 95%, b. 90%, c. 99%

Instead of being expressed as a percentage, the confidence level is expressed as a proportion using the confidence coefficient. For instance, the confidence coefficient would be. 99 if you had a confidence level of 99%. In general, the greater the coefficient, the more confident you can be in the accuracy of your findings.

The most typical levels of confidence are 90%, 95%, and 99%. A summary of the values corresponding to these typical confidence levels can be seen in the following table. The "confidence coefficient" is simply the confidence level presented as a proportion .

for a:

Z1=a/2=1.96

1-a/2=0.975

a=0.05

so,

(1-a)x100

=95%

Hence, the level of confidence is 95%

for b:

Z1=a/2=1.645

1-a/2=0.95

a=10

so,

(1-a)x100

=90%

Hence, the level of confidence is 90%

for c:

Z1=a/2=2.576

1-a/2=0.995

a=0.01

so,

(1-a)x100

=99%

Hence, the level of confidence is 99%

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a) The algebraic expression for the coordinates of point L is (a-b,b).

b)The value of a is 9, and the value of b is 3

What are coordinate points?

A specific point on a grid referred to as a coordinate plane can be located using coordinates, which are two numbers. In a plane, a point is known to have specific coordinates. The coordinates are the ordered pairs of numbers (x, y) that describe the location of any point on a plane. In our everyday lives, we use coordinates for things like map location, classroom seating, and more.

a) Extending point L towards the y-axis, we see that it corresponds to the given coordinate, i.e., (0,b). Therefore the y coordinate is b.

Next, extending the point L towards the x-axis, we see that the point lands somewhere between the distance 'a' from the origin. As the height is 'b', and as the trapeziums are identical, we can say that the extended point of L lands at a point that is 'b' distance from 'a'. Hence the x coordinate is a-b.

Hence, the coordinates of point L are (a-b,b).

b) Given M(9,9) and N(15,15).

Extending the point M towards the x-axis, we get that it coincides with the point 'a', therefore we get the value of a=9.

Now extending point N towards the x-axis, we get that it lands at a distance of 15 from the origin. We got the value of a=9, so the remaining distance between the point (9,0) and (15,0) is 6 units.

Extending the point (9,0) upwards, we see that it cuts the uppermost trapezium giving us the distance of the trapezium excluding the small triangle formed. Now taking the same information, if we cut the bottom-most trapezium, we see that it cuts at point (6,0).

Now we know the height of the trapezium is 'b'. So, we get b=9-6 (as 9 is the distance of the entire trapezium, and 6 is from the above calculations).
We get b=3.

Hence we got the value of 'a'=9 and 'b'=3.

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To make this mixture 60% cashews, 240 pounds of cashews must be added to 36 pounds of this mixture.

For the stated question-

Let the total amount of mix be 'x'.

45% of the mix is cashew nuts: 0.45x.

Now, 60% cashews is made by making 36 lb; 0.60x.

Then, 0.45x + 36 = 0.6x

x = 36/0.15

x = 240

Thus, 240 pounds of the cashews should be added to 36lb of this mix to get a mix that is 60% cashews.

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Answer:

10.35 miles/hour

Step-by-step explanation:

Hence, Sam ran at the rate of 10.35 miles/hour .

The probability that the average score of golfers exceeded = 0.0228

A measurement of a data set's deviation from the mean is referred to as "standard deviation.". A low standard deviation means that the data are grouped around the mean, whereas a large standard deviation says that the data are more spread out.

According to the given information

We are given that,

[tex]& \mu=80 \\[/tex]

[tex]& \sigma=3.5 \\[/tex]

[tex]& n=49 \\& \mu \bar{x}=\mu=80 \\[/tex]

[tex]& \sigma \bar{x}=\sigma / \sqrt{n}=3.5 / \sqrt{ } 49=0.5 \\& P(\bar{x} > 81)=1-P(\bar{x} < 81) \\& =1-P[(\bar{x}-\mu \bar{x}) / \sigma \bar{x} < (81-80) / 0.5] \[/tex]

[tex]& =1-P(z < 2) \\&[/tex]

Using standard normal table

[tex]& =1-0.9772 \\& =0.0228[/tex]

Probability [tex]$=0.0228$[/tex]

The probability that the average score of golfers exceeded = 0.0228

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The correlation of two pairs of data values tells about the degree of movement that can occur. The correct option is A, C, and D.

The degree of movement that can occur in one of the data values when another data value is increased or decreased is indicated by the correlation of two pairs of data values.

A.) There is a positive relationship between depth under water and pressure.

Because water pressure increases with depth, this is a casual relationship that can be observed while swimming in a deep swimming pool.

C.) A positive relationship between the age and weight of a puppy.

This is a casual relationship because the puppy's weight and size both increase as it grows.

D.) A negative relationship between temperature and the number of snowboards sold

This is a casual relationship because as the weather warms up, fewer people prefer to go snowboarding.

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a) The minimum number of hikers who could have walker between 6 and 17 miles is of: 9.

b) The maximum number of hikers who could have walker between 6 and 17 miles is of: 19.

The frequency table shows the number of times that each range was observed in this problem.

For the minimum number of hikers walking between 6 and 17 miles, we have that:

Hence the minimum number is of 9, all of which walked between 10 and 15 miles, which is between 6 and 17.

For the maximum number of hikers walking between 6 and 17 miles, we have that:

Hence the maximum number is of:

2 + 9 + 8 = 19.

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Answer:

To solve this problem, we can set up the following system of equations:

Let x be the rate at which Joe flew in still air and y be the rate of the wind.

1000 km / 4 hours = x + y

700 km / 7 hours = x - y

Solving this system of equations using the elimination method, we get:

x + y = 250

x - y = 100

Adding these two equations together, we get 2x = 350, so x = 175 km/hour.

Subtracting the second equation from the first equation, we get 2y = 150, so y = 75 km/hour.

Therefore, the rate at which Joe flew in still air is 175 km/hour and the rate of the wind is 75 km/hour.

Step-by-step explanation:

where log is the base-10 logarithm and [H+] stands for the hydrogen ion concentration in units of moles per liter solution.

pH=−log([H3O+])

=−log(8.25×10−3)

=−log(8.25)−log(10−3) loga(xy)=loga(x)+loga(y)

=−log(8.25)+1 log(10x)=x

=0.0 round off to one decimal place

where,

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It follows that someone who watches TV for 11 hours can complete 19 situps.

This information was provided to us by the question.

A linear equation in slope-intercept form is one with the formula y = ax + b.

Claim: A line with slope a contains the point (0,b) on the y-axis and the solutions of the equation y = ax + b (where a and b are numbers) form a line with slope a.

a=−1.077

b=30.98

r2=0.744769

r=−0.863

Where

X is the amount of situps.

Y is the quantity of television viewing hours.

X equals 11, so

Including this in the existing formula

Y = (-1.077)(11) + 30.98

Y = −11.847 + 30.98

Y = 19.133

which equals around 19

So, it follows that someone who watches TV for 11 hours can complete 19 situps.

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The measure of AB in the figure is C. 100 degree

The measure of AB in the figure is the length of arc, this is given by the formula

given angle / 360 * 2πr

However, the measure in degree is equal to the angle given which is 100 degree.

The size or the measure of the angle is same at any point within same lines that formed the angel AB.

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A= -10140000  B= 3485800  C= 13414200

Step-by-step explanation: hope this helped!!!

Step-by-step explanation:

-8x-8 = -49.44+ 8x+12y=58.20