help! offering 15 points

Answer:[tex]\sqrt{\frac{14}{5} }[/tex]  or [tex]\frac{\sqrt{70} }{5}[/tex]

Step-by-step explanation:

(f o g )(x) means f(g(x)) so take g(x) and put it into f every time you see an x

f(g(x))[tex]=\sqrt{\frac{2(4+\sqrt{x} )}{5} }[/tex]

now plug in 9 for this answer  =[tex]\sqrt{\frac{14}{5} }[/tex]  or [tex]\frac{\sqrt{70} }{5}[/tex]

The probability of no tails is 20% which is option A.

in order to  calculate the probability of no tails in the question, al we have to do is  to add   the frequency of the outcome given which are the  "Heads, Heads" that is  two heads in a row:

Probability(No Tails) = Frequency of head, Head divide by / Total frequency

The Total frequency is 40 + 75 + 50 + 35 = 200

Therefore,  we can say that  P(No Tails) = 40/200 = 0.2 or 20%

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Step-by-step explanation:

Mohan said, "My brother arrived home late." (Change the sentence into reported speech).

The relationship between pints and cups where p represents pints and n represents cups is n = 2p.

We have,

3 cups converts to 1.5 pints

and 5 cups converts to 2.5 pints.

We know from constant of proportionality

y = kx

k = y/x

Put y= 2.5 and x= 5

Then, k = 5/2.5

k = 2

So, the relationship between pints and cups where p represents pints and n represents cups is

n = 2p

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The amount of paint  needed to cover silo with radius of 3 and height of 12 is  0.64π

To calculate the amount of paint needed to cover the silo, we need to find the surface area of the silo first.

The surface area of the curved part of the silo (excluding the top and bottom) can be calculated using the formula:

A = 2πrh

where:

r is the radius of the silo and

h is the height of the silo.

Plugging in the values, we get:

A = 2π(3)(12)

A = 72π

The surface area of the top and bottom of the silo can be calculated using the formula for the area of a circle:

A = πr^2

Plugging in the value of the radius, we get:

A = π(3)^2

A = 9π

To get the total surface area of the silo, we need to add the surface area of the curved part and the surface area of the top and bottom:

Total surface area = 72π + 9π = 81π

To calculate the amount of paint needed, we need to divide the total surface area by the coverage area of one gallon of paint. Let's assume that one gallon of paint can cover 400 square feet.

Amount of paint needed = Total surface area / Coverage area per gallon

Amount of paint needed = (81π) / 400

Amount of paint needed = 0.64π

Therefore, approximately 0.64π gallons of paint are needed to cover the silo.

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Answer: Starting with 2(tan x - sqrt(3)) = 2:

First, divide both sides of the equation by 2 to simplify:

tan x - sqrt(3) = 1

Next, add sqrt(3) to both sides:

tan x = 1 + sqrt(3)

To solve for x, we need to take the arctan of both sides:

x = arctan(1 + sqrt(3))

In degrees, this is:

x = 75 degrees

In radians, this is:

x = 5π/12 radians

Step-by-step explanation:

The function is solved for the given intervals and the values are noted

Given data ,

Let the function be represented as f ( x )

when x ≤ -2 , f ( x ) = -2

when -2 ≤ x ≤ 2 , f ( x ) = - ( x + 1 )²

And , when x > 2 , f ( x ) = - ( 1/4 )x + 1

Now , the function is defined as

a)

f ( -2 ) = -2

b)

f ( -1 ) = - ( -1 + 1 )²

f ( -1 ) = 0

c)

f ( 3 ) = ( -1/4 )(3 ) + 1

f ( 3 ) = -3/4 + 1

f ( 3 ) = 1/4

Hence , the function is solved

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Bulk Pete's has the smaller unit price, so that coffe has the better price.

First, we know that five pounds of Kroger Dark Ground at $17.81, then the cost of a single pound of this cofee is given by the quotient:

$17.81/5 lb = $3.56 per lb.

That is the unit price of this coffe

While we know that Bulk Pete's Italian Roast at $3.11 per pound.

So we already can see that Bulk Pete's coffec has a smaller cost per pound, so that one has the better price.

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Therefore, the expression -8mx²-9m +45 has two real solutions for any value of m.

In mathematics, an expression is a combination of numbers, symbols, and operations that represent a value or a quantity. Expressions can be simple, such as a single number or variable, or they can be complex, consisting of multiple terms and operations. Expressions can involve a variety of mathematical operations, including addition, subtraction, multiplication, division, exponents, and roots. They can also include parentheses, brackets, and other symbols to indicate the order of operations or to group terms together. Expressions are commonly used in mathematical equations and formulas, and they are also used in programming languages and computer science to represent calculations and algorithms.

Here,

The expression -8mx²-9m +45 is a quadratic expression in the variable x, where m is a constant. When we set this expression equal to zero and try to solve for x, we get the quadratic equation:

-8mx² - 9m + 45 = 0

This is a quadratic equation in standard form, where the coefficients a = -8m, b = -9m, and c = 45. To determine the number and type of solutions, we can use the discriminant:

=b² - 4ac

= (-9m)² - 4(-8m)(45)

= 81m² + 1440m

The discriminant is positive for all values of m, so there are always two real solutions to this quadratic equation.

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We can be 90% confident that the true population proportion lies between 0.433 and 0.567.

In statistics, proportion refers to the percentage or fraction of a population or sample that possesses an important trait.

If we wanted to know, for instance, what percentage of individuals in a particular city possessed cars, we would pick a sample of people from that city, count how many of them did, and express that number as a percentage of the whole sample size.

When drawing conclusions about a wider population from a sample, proportions are frequently used. Based on the sample proportion, one can estimate or evaluate the population proportion using confidence intervals and hypothesis tests.

A range of values used to estimate or define a population parameter, such as a mean, percentage, or variance, is referred to in statistics as an interval. The lower and upper bounds of an interval estimate are determined using the sample data and a degree of confidence or probability.

For instance, a range of values near the sample mean that we may reasonably be convinced contains the true population mean would make up a confidence interval for the population mean. The margin of error reveals the accuracy of the estimate, while the confidence level shows the likelihood that the interval contains the actual population mean.

According to question,

We can apply the following formula to create a confidence interval for a population proportion:

Confidence Interval is calculated as Sample Proportion +/- Error Margin.

where the margin of error takes into account the uncertainty in calculating the population proportion from the sample proportion and the sample proportion is the portion of the sample that possesses the feature of interest.

The sample proportion in this instance is:

x/n = 75/150 = 0.5

The following formula can be used to determine the margin of error:

Error margin is equal to z*√(p(1-p)/n)).

where z is the desired level of confidence's associated z-score. Using a typical normal distribution table, the z-score is 1.645 with a 90% degree of confidence.

When we enter the values, we obtain:

1.645√(0.5(1-0.5)/150) = 0.067 is the margin of error.

the 90% confidence interval for the population proportion is:

0.5 +/- 0.067, or (0.433, 0.567)

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The graph of y = -f(x + 2) - 1 when transformed from the graph of y = f(x) is added as an attachment

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

The graph of y = f(x)

To sketching the graph of y = -f(x + 2) - 1, we use the following steps:

See attachment for the transformed graph

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To get the numbers and their values we must match the circles directly linked to a number with values whose summation equals the assigned number.

We can get the numbers and their reasons as follows:

1 equals 4 because the numbers directly connected to figure one in the circles are 3 and 4.

2 equals 12 because the numbers directly linked to the number two are 8 and 4.

3 equals 7 because the numbers directly linked through the circles are 3 and 4.

The number 4 is 8 because the number directly linked to it is 8.

Finally, the number 5 is 5 because 4 and 5 are directly connected.

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We can conclude that the ratio of juniors to adults is 9:5 respectively.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.

A proportion is an equation that sets two ratios at the same value.

For instance, you may express the ratio as 1: 3 (there are 3 girls for every boy) if there is only 1 boy.

There are 1 in 4 boys and 3 in 4 girls.

So, we know that:

Juniors to children = 3:5

Children to adults = 3:1

Now, calculate the ratio of Junoirs to adults as follows:
J:C = 3:5
C:A = 3:1

Then,

J:C:A

3:5:5

3:3:1

Add, and we get:
9:15:5

The ratio of juniors to adults is 9:5.

Therefore, we can conclude that the ratio of juniors to adults is 9:5 respectively.

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To find the equation of a line perpendicular to d: 3x − 6y = 1, we need to determine its slope. We can rewrite d in slope-intercept form as:

y = (1/2)x - 1/6

The slope of d is then 1/2. A line perpendicular to d will have a slope that is the negative reciprocal of 1/2:

slope of perpendicular line = -2

Since the line passes through (0, 7), we know that when x = 0, y = 7. We can use this point and the slope of the line to find its equation using point-slope form:

y - 7 = -2(x - 0)

y - 7 = -2x

2x + (y - 7) = 0

2x + (y - 7) = c

where c is a constant.

To find the value of c, we need another point on the line. Since the line is perpendicular to d, we know that their intersection point will be the midpoint between (0, 7) and the x-intercept of d. To find the x-intercept of d, we let y = 0:

3x - 6(0) = 1

x = 1/3

So the midpoint between (0, 7) and (1/3, 0) is:

((0 + 1/3)/2, (7 + 0)/2) = (1/6, 7/2)

This point lies on the line, so we can substitute its coordinates into the equation 2x + (y - 7) = c:

2(1/6) + (7/2 - 7) = c

1/3 = c

Therefore, the value of c is 1/3. The equation of the line passing through (0, 7) and perpendicular to d: 3x − 6y = 1 is:

the value of c is 1/3. The equation of the line passing through (0, 7) and perpendicular to d: 3x − 6y = 1 is:2x + (y - 7) = 1/3

The value of c=7.

The equation of a straight line is given by y = mx + c where m represents the slope of the line and c is the height at which the line crosses the y-axis.

The equation of the given line is l:2x+by=c and it is perpendicular to d:3x-6y=1 and also the given line l passes through point (0,7)

The slope of two mutually perpendicular lines is related as per the following formula:

m1*m2=-1

Slope for line d = 1/2. Therefore, m*(1/2)=-1

i.e. slope of line l will be m=-2.

So, the given equation becomes [tex](y-y_1)=m(x-x_1)[/tex]

[tex](y-y_1)=-2(x-x_1)[/tex]

For point (0,7) the equation will be

[tex](y-7)=-2(x-0)[/tex]

y=-2x+7

Upon comparing the obtained values will be b=1 and c=7

Hence, the value of c will be 7 for the given equation.

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All the rays in tiffany's designs that she is going to use on a stained glass window above her front door are EA , ED , EB , GC GH

Rays are a part of a line that has a fixed starting point but no endpoint.

Rays are written in a specific form

first letter should be the fixed point and the second letter should be point with no endpoint

E is fixed point A is no end point = EA

E is fixed point D is no end point = ED

E is fixed point B is no end point = EB

G is fixed point C is no end point = GC

G is fixed point H is no end point = GH

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The school bookstore originally ordered 500 three ring notebooks.

Information given in the problem:

This helps to deduce that

The equation set up

Assuming the original order quantity of three ring notebooks is x, then

0.20 * (0.25 * x) = 25

Solving for x

0.20 * (0.25 * x) = 25

1/20 * x = 25

x = 25 * 20

x = 500

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Answer:

To solve this, we can use the following formula:

FV = PV * (1 + r/n)^nt

Where:

FV = Future Value

PV = Present Value

r = Interest Rate

n = Number of times interest is compounded per year

t = Number of years

In this case, we have the following information:

FV = $14,000

r = 4.5%

n = 12 (monthly compounding)

t = 3 years

We can solve for PV as follows:

PV = FV / (1 + r/n)^nt

PV = $14,000 / (1 + 0.045/12)^12*3

PV = $8,000.00

Therefore, the amount of money that should be deposited today in an account that earns 4.5% compounded monthly so that it will accumulate to $14,000 in 3 years is $8,000.00.

Step-by-step explanation:

The measure of each arc.

arc AE= 103°

arc ACE= 257°

arc GDC= 196°

arc BHC= 305°

arc FD= 79°

arc FBD= 281°

What is meant by measure?

Measure refers to the quantity or size of something, often expressed in numerical terms, such as length, weight, volume, or time. It helps to provide a standard for comparison or evaluation.

What is meant by arc?

An arc is a curved portion of a line or circle that is defined by two endpoints and the points along the curve between them. It is often used in geometry and trigonometry.

According to the given information

Here are the measures of each arc:

arc AE = (17+26+28+32)° = 103°

arc ACE = (66+55+89+47)° = 257°

arc GDC = (28+32+47+89)° = 196°

arc BHC = (66+17+26+28+32+47+89)° = 305°

arc FD = (32+47)° = 79°

arc FBD = (28+26+17+66+55+89)° = 281°

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Answer:

D) 4 x 3/4 = 12/4 = 3

Step-by-step explanation:

The object that matches the description is C.

Properties of a parallelogram.

A parallelogram is a four sided shape which has a pair of slant sides, though a pair of opposite sides are equal. It has some other unique properties that differentiate it from other four sided figures.

A circle is a figure that is bounded by a curved side called its circumference. Its diameter is twice of its radius.

From the information given in the question, it can be deduced that the best object that matches the description is object C.

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The measure of ∠HKI is equal to 73 degrees.

In Mathematics and Geometry, the theorem of intersecting chord states that when two (2) chords intersect inside a circle, the measure of the angle formed by these chords is equal to one-half (½) of the sum of the two (2) arcs it intercepts.

By applying the theorem of intersecting chord to this circle shown in the image attached above, we can infer and logically deduce that angle a can be calculated by using this formula:

m∠HKI = ½(b + c)

m∠HKI = ½(105 + 41)

m∠HKI = ½(146)

m∠HKI = 73°.

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The requried ball reached a maximum height of approximately 62 feet

Let the ball is thrown vertically upward, we can use the following formula to find the maximum height it reaches:

[tex]h(t) = -16t^2 + vt + h_0[/tex]

here, h(t) is the height of the ball at time t, v is the initial velocity of the ball (in feet per second), and h0 is the initial height of the ball (in feet). We can also use the fact that the ball remains in the air for 3.8 seconds, which means that the time it takes to reach the maximum height is half of that or 1.9 seconds.

At the highest point, the ball's velocity is zero, so we can find the initial velocity by setting v = 0 in the above formula and solving for h₀:

h₀ = h(t) + 16t²

   = 4 + 16(1.9)²

   ≈ 4 + 57.76

   ≈ 61.76

Therefore, the ball reached a maximum height of approximately 62 feet

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the answer is

option A

Step-by-step explanation:

(2√3)/3

Therefore, the probability of selecting two Democrats and two Republicans from a committee of four people is approximately 0.476 or 47.6%.

To find the probability of selecting two Democrats and two Republicans from a committee of four people out of a city council consisting of five Democrats and five Republicans, we can use the formula for probability:

Probability = (number of ways to select two Democrats and two Republicans) / (total number of ways to select any four people)

The number of ways to select two Democrats and two Republicans can be found by multiplying the number of ways to select two Democrats from the five available Democrats and the number of ways to select two Republicans from the five available Republicans. This can be expressed as:

(Number of ways to select 2 Democrats from 5 Democrats) * (number of ways to select 2 Republicans from 5 Republicans)

= (5 choose 2) * (5 choose 2)

= 10 * 10

= 100

The total number of ways to select any four people from the city council is:

(Number of ways to select 4 people from 10 people)

= (10 choose 4)

= 210

Therefore, the probability of selecting two Democrats and two Republicans is:

Probability = (number of ways to select two Democrats and two Republicans) / (total number of ways to select any four people)

= 100 / 210

= 10 / 21

≈ 0.476 or 47.6% (rounded to the nearest tenth)

Therefore, the probability of selecting two Democrats and two Republicans from a committee of four people is approximately 0.476 or 47.6%.

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Answer:

Graph B

Step-by-step explanation:

Graph B is not a function, because it fails the "vertical line test". Which means the plots that would be placed on the line intersecting the X axis would have the same X value, and X values CANNOT repeat when it comes to functions. So the Answer is B because the X Values would repeat if you were to write the coordinates of the points down.

Answer:

A = 383 [tex]\frac{1}{4}[/tex] m²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

   = [tex]\frac{1}{2}[/tex] × 42 × 18 [tex]\frac{1}{4}[/tex] ( change mixed number to improper fraction )

  = 21 × [tex]\frac{73}{4}[/tex]

  = [tex]\frac{21(73)}{4}[/tex]

   = [tex]\frac{1533}{4}[/tex]

  = 383.25

 = 383 [tex]\frac{1}{4}[/tex] m²

The required width of the aquarium is 1.5033 feet.

To find the width of the aquarium, we can use the formula for the volume of a rectangular prism:

Volume = Length x Width x Height

We are given the length and height of the aquarium, as well as its volume (33.75 gallons). However, the volume is in gallons, while the dimensions are in feet. We need to convert the volume to cubic feet so that we can use the formula.

1 gallon is equivalent to 0.13368 cubic feet (approximately). Therefore, we have:

Volume = 33.75 gallons x 0.13368 cubic feet/gallon

Volume = 4.51 cubic feet

Now we can substitute the given values into the formula and solve for the width:

4.51 cubic feet = 2 feet x Width x 1.5 feet

Simplifying the equation, we have:

Width = 4.51 cubic feet / (2 feet x 1.5 feet)

Width = 1.5033 feet (rounded to four decimal places)

Therefore, the width of the aquarium is approximately 1.5033 feet.

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Upon answering the query  As a result, triangle  side C is around 13 metres long.

A triangle is a polygon since it has three sides and three vertices. It is a basic geometric shape. A triangle with vertices A, B, and C is referred to as Triangle ABC. In Euclidean geometry, a single plane and triangle are obtained when the three points are not collinear. If a triangle has three sides and three corners, it is a polygon. The triangle's corners are the places where its three sides intersect. Three triangle angles add up to 180 degrees.

B is given to be 7.5mm and C is given to be 11mm. The task is to determine angle B. A diagram of the triangle is shown below:

       C

      /|

     / |

 b /  | a

   /   |

  /__|

  A  c B

The sine ratio can be used to determine angle B:

[tex]sin(B) = b/c\\sin(B) = 7.5/11\\B = sin^{-1}(7.5/11)\\B =42[/tex]

As a result, angle B is around 42°.

B is stated as 17.5 degrees, and c is provided as 9.33 cm. The task is to locate b. A diagram of the triangle is shown below:

       C

      /|

     / |

 b /  | a

   /   |

  /____|

  A  c B

[tex]sin(B) = b/c\\b = c sin(B)\\b = 9.33 sin(17.5)\\b =2.65 cm\\[/tex]

As a result, side B is around 2.65 cm.

It is said that A = 32° and a = 25 m. Our task is to locate c. A diagram of the triangle is shown below:

       C

      /|

     / |

 b /  | a

   /   |

  /____|

  A  c B

[tex]sin(A) = c/a\\c = a sin(A)\\c = 25 sin(32)\\c = 13 m\\[/tex]

As a result, side C is around 13 metres long.

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The actual length of roof of house is 25 feet.

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

From the given figure, model has 24 inches and roof has 15 inches and the base angle of roof is 37°.

The actual house dimension is 40 feet.

40 feet = 480 inches

a) Scale factor = 24/480

= 1/20

So, measure of actual roof is 1/20 = 15/x

x=300 inches

300 inches = 300/12 = 25 feet

b) Using cosine rule formula

25=√(40²+25²-2×40×25 cosC)

625=2225-2000cosC

-1600=-2000cosC

cosC=4/5

cosC=0.8

∠C=37°

Therefore, the actual length of roof of house is 25 feet.

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