the data given to the right includes data from 37 candies, and 5 of them are red. the company that makes the candy claims 30% of its candies are red. use the sample data to construct a 95% confidence interval estimate of the percentage of red candies. what do you conclude about the claim of 30%?

The measurements 15, 17, 22 do not form a right triangle.

In this question, we have the measurements 15, 17, 22

We check whether the measurements 15, 17, 22 is Pythagorean triple.

22^2 = 484

15^2 = 225

17^2 = 289

15^ + 17^2 = 225 + 289

                = 514

                ≠ 484

i.e., 15^ + 17^2 ≠ 22^2

This means, these measurements do not form a right triangle.  

Therefore, the measurements 15, 17, 22 do not form a right triangle.

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The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B  t = ln(3) / 0.05

Given,

The population of a city can be modeled using the formula P=100,000e^(0.05t)

t is the number of years after 2012

P is the population of the city

We have to find the equation that can be used to find the number of years after 2012 that the population will triple to 300,000.

Here,

Substitute 300000 in for P and solve for t

300000=100000e^0.05t

Divide both sides by 100000:

We get,

3 = e^0.05t

Multiply both sides by the natural log (ln)

Then,

ln(3) = 0.05t

Now, divide 0.05 on both sides to get t by its self

t = ln(3) / 0.05

Therefore,

The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B  t = ln(3) / 0.05

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The exponential function that approximates the number of fruit flies on the banana after x days is y = 7 x 1.3ˣ.

An exponential function is a mathematical function form of y = aⁿ or y = abˣ, where b is a constant or the base of the function, a is a variable, and n is the variable exponent.

Exponential functions must always contain an exponent, which is an integer raised to some power.

When the exponent is positive, it implies the function is increasing in value and vice versa.

Percentage increase per day = 30%

The number of fruit flies found = 7

The number of days = x days

Let the number of flies after x days = y

y = 7 x 1.3ˣ

Thus, an exponential representation of the function which Emma can use to model the number of fruit flies after x days is y = 7 x 1.3ˣ.

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Answer:

Step-by-step explanation:

Thanks

Answer:

12.3459 grains

Step-by-step explanation:

Answer:

12.346 grains

Step-by-step explanation:

for an approximate result, multiply the mass value by 15.432

( which is basically 0.8 times 15.432)

The coordinate plane that represents both lines as well as the solution of the system is shown in the diagram below.

The solution to a system of equations is the value of x and y that will make the equations of the system true if they are plugged in into either of the two equations in the system.

Thus, when the equations or functions are plotted as a line on a coordinate grid, the system intersect at a point The coordinates of this point is the solution of the system of equations.

The function for Gary, y = 2x - 5, would be a line that has a slope of 2 and cuts the y-axis at -5, while that of Genevieve y = -3x + 4 will have a slope of -3, and will intercepts the y-axis at 4.

The red line in the coordinate grid in the image below is Gary's function y = 2x - 5, while the blue line is that of Genevieve y = -3x + 4. They bot intersect at (1.8, -1.4).

The solution is: (1.8, -1.4).

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Answer:

x = 12 m

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

here A = 44 , then

x × 3 [tex]\frac{3}{4}[/tex] = 44 ( change mixed number to improper fraction )

x × [tex]\frac{11}{3}[/tex] = 44 ( multiply both sides by 3 to clear the fraction )

11x = 132 ( divide both sides by 11 )

x = 12 m

The exponential function that can model the county population, y, x decades after Tiana was born, is:

[tex]y = 641000(0.99)^x[/tex]

The population will fall below 600,000 in 6.6 decades after Tiana was born.

The definition of the exponential function is presented as follows:

[tex]y = a(b)^x[/tex]

In which the parameters of the exponential function are presented as follows:

In the context of this problem, the values of these parameters are given as follows:

Hence the function is:

[tex]y = 641000(0.99)^x[/tex]

The population will fall below 600,000 when y = 600000, hence:

[tex]y = 641000(0.99)^x[/tex]

[tex]600000 = 641000(0.99)^x[/tex]

[tex](0.99)^x = \frac{600000}{641000}[/tex]

[tex]\log{(0.99)^x} = \log{\left(\frac{600000}{641000}\right)}[/tex]

[tex]x\log{0.99} = \log{\left(\frac{600000}{641000}\right)}[/tex]

[tex]x = \frac{\log{\left(\frac{600000}{641000}\right)}}{\log{0.99}}[/tex]

x = 6.6 decades.

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Answer:

It's option B, (f • g)(x) = 3x^3 + 6x^2 - 5x - 10

Step-by-step explanation:

In this problem, we are dealing with a branch of functions called composite functions. What the difference is between normal and composite functions is that we instead of defining a value for f(x), take two functions, f(x) and g(x), in the form of f and g. For instance, h(x) = g.

• Take the products of both functions.

f(x)g(x) = 3x²+5 • x-2

• Next, expand the functions. We expand by combining like terms.

= 3x^3 - 6x^2 + 5x - 10

Since the function cannot be simplified further, this leads to option B being our answer.

Hope this helps!

The correct statement that is a combination of both conditional statements is;  X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides.

A triangle is defined as a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees.

We are given the conditional statements as;

X → Y: If the sum of the interior angles of a shape is 180°, then it's a triangle.

Y → Z: If a shape is a triangle, then it has three sides.

Now, transitive property states that “if two quantities are equal to a third quantity, then we can say that all the quantities are equal to each other”.

Thus, applying transitive property to our given statements we can say that;  X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides.

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The equation of the parallel line is y = (-3/2)x + 20

What does the term Slope of a Straight Line means?

A line's slope is defined as the change in y coordinate with respect to the change in x coordinate. The net y coordinate change is y, while the net x coordinate change is x.

Solution:

Firstly we need to find the slope of the given line 3x+2y = 14

Since, the equation is in the form ax + by = c

Therefore, by comparing we can say a = 3 and b = 2

Slope = -(b/a) = -3/2

Since we need to find the equation of the parallel line

So, the slope of the parallel line will be -3/2

y = mx + b

we know that the line passes through the point (8,8)

putting x,y = 8 and m = -3/2

8 = (-3/2)*8 + b

8 = -12 + b

b = 20

So, the equation of the parallel line is y = (-3/2)x + 20

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Answer:

Answer is b

Step-by-step explanation:

Because

The y-intercept of the line will be equal to 7.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that a line that has a slope of 2 and ( - 2, 3 ). The y-intercept of the line will be calculated as,

y = mx + c

3 = (-2 x 2 ) +c

3 = -4 + c

c = 4 + 3

c = 7

Therefore, the y-intercept of the line will be equal to 7.

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Answer:

x=1 y=3

Step-by-step explanation:

By looking at the equations, you can use substitution

Set the equation equal to y

y=-5x+8

y=-2x+5

Then put equation together

-5x+8=-2x+5

Move numbers over

3x=3

x=1

Put x back into equation

5+y=8

2+y=5

y=3

Using the triangle rule, the length of the third side falls between 5 cm and 29 cm.

In the given question,

The measurements of two sides of a triangle are 12 cm and 17 cm.

We have to find which side length could be the measurement of the third side of the triangle.

We know that,

The sum of the length of any two sides is always greater than the third side.

The given sides of triangles are 12 cm and 17 cm.

Hence, the length of the third side should be shorter than the total of the other two sides,

12 + 17 = 29 cm.

Considering that the third side must be less than the difference between the first two sides,

17 – 12 = 5 cm

So, the length of the third side falls between 5 cm and 29 cm.

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Answer: I would say a half of beef is cheaper the pounds are different maybe subtract a half from five

Step-by-step explanation:

0.065=x/5800

x=$377; that is the dollar value of the decrease

The account is now worth $5423.

The number line with the numbers -3, 1 and 3 is shown by the image at the end of the answer.

The correct statements regarding the number line are given as follows:

Integer numbers are numbers that do not have decimal parts, they are either positive or negative, but exact.

These numbers are plotted marking a symbol such as a X or a circle on the number line.

The number line is increasing, so the negative numbers appear before the positive numbers.

This means that if a number a is to the left another number b, the number a is less than b, hence:

As the order in which the numbers appear is given as follows:

-3, 1 and 3.

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The linear equation we need to solve is:

$25.50*w = $309.99 - $131.49

And the solution is w = 7.

We know that the cost of the gaming chair is $309.99.

To buy this, you already have saved $131.49, and save another $25.50 per week, then the amount you have after w weeks is:

f(w) = $131.49 + $25.50*w

So the linear equation we need to solve is:

$131.49 + $25.50*w = $309.99

To solve this we need to isolate w.

$131.49 + $25.50*w = $309.99

$25.50*w = $309.99 - $131.49

w = ($309.99 - $131.49)/$25.50 = 7

So they can buy the chair after 7 weeks.

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The values of each variable are ∠d=71°, ∠c=87°, arc a=121°, arc b=53°.

A circle is a shape formed by all points on a plane that are at a fixed distance from the center. It is the curve sketched out by a point moving in a plane such that its distance from a particular point remains constant. The radius is the distance between any point on a circle and the center. The radius must usually be a positive integer. Degenerate case is a circle with r=0. Except when otherwise specified, this article is about circles in Euclidean geometry, and specifically the Euclidean plane.

1) Measure of ∠d

∠d+109°=180°

∠d=71°

2) Measure of ∠c,

∠c+93°=180°

∠c=87°

3) Measure of arc a is,

109°=1/2[97°+arc a]

218°=97°+arc a

arc a=121°

4) Measure of arc b,

87°=1/2[121°+arc b]

174°=121°+arc b

arc b=53°

Therefore, the values of each variable are ∠d=71°, ∠c=87°, arc a=121°, arc b=53°.

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The standard deviation of the sampling distribution is 0.01767.

Standard deviation is a measure of the amount of variability or spreads in a set of data.

It is calculated as the square root of the variance and is often denoted by the symbol σ (sigma) for a population and s for a sample.

We have,

Given that the sample size is sufficiently large (n=400) and the population proportion is known, we can use the formula for the standard deviation of the sampling distribution of the sample proportion, which is:

[tex]\sigma_{\hat{p}} = \sqrt((p (1 - p)) / n)[/tex]

where p is the population proportion and n is the sample size.

In this case,

p = 0.53 (as given in the problem) and n = 400.

Substituting these values into the formula, we get:

[tex]\sigma_{\hat{p}} = \sqrt((0.53 (1 - 0.53)) / 400)\\\sigma_{\hat{p}} = \sqrt((0.53 0.47) / 400)\\\sigma_{\hat{p}} = \sqrt(0.0003121)\\\sigma_{\hat{p}} = 0.01767[/tex]

(rounded to five decimal places)

Therefore,

The standard deviation of the sampling distribution is 0.01767.

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On Wednesday 1/6 of the patio area is left to tile

Let the patio area be x

On Monday, he tiled 1/3 of his patio = 1/3 x

on Tuesday, he tiled 1/2 of the patio area = 1/2 x

The area left to tile on Wednesday

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

x - 1/3 x - 1/2 x

(6x - 2x - 3x)/6

= 1/6 x

The area left to tile on Wednesday is 1/6 of the patio area

Therefore,  1/6 of the patio area is left to tile on Wednesday

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The value of (-42n+28p)(-1/4) is 249n/4

A fraction represents a part of a whole or, more generally, any number of equal parts. A fraction describes how many parts of a certain size there are, for example, one-half, three-fifths, three-quarters.

A fraction has a denominator and numerator. There are three types of fraction. Proper, improper and mixed fraction

Opening the parentheses of the equation

(-42n+ 28p)(-1/4).

= -42n× -1/4+ 28× -1/4

= (42n×-7)/4

= -294n/4

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Answer:

Step-by-step explanation:

Yes, you did it right.

The probability that both bills are $20 if the first selected is a $20 bill is 1/16.

The probability formula is as defined as the possibility of any event to happen which comes to be equal to the ratio of the number of favourable outcomes and the total number of outcomes.

Probability of event to occur P (E) =

[tex]\frac{Number of favourable outcomes}{ Total number of outcomes }[/tex]

Hat contains four bills: a $1, a $5, a $10, and a $20 bill.

Probability(P1) of Getting $20 bill in 1st selection = 1/4 ;

After Replacement,

Probability(P2) of Getting $20 bill in 2nd selection = 1/4 ;

So, the probability that both bills are $20 if the first selected is

a $20 bill = 1/4 * 1/4 = 1/16,

Hence we get 1/16 as the probability of getting both bills of $20.

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Answer: mode is 94

Step-by-step explanation:

By using the concept of differentiation, it can be calculated that

value of P is -2 and value of Q is 1

What is differentiation?

Differentiation is the process where  the instantaneous rate of change of function can be calculated based on one variable. Differentiation is a very important tool in calculus

Here differentiation is used

f(x) = [tex]x^2y[/tex]

[tex]df = 2xydx+x^2dy[/tex]

Here P = 2xy, Q = [tex]x^2[/tex]

At x = 1, y = -1

P = 2(1)(-1) = -2

Q = [tex](-1)^2[/tex] = 1

So value of P is -2 and value of Q is 1

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Answer:

[tex]-1.35[/tex] is bigger (larger)

Step-by-step explanation:

[tex]-1\frac{4}{9}=-1.\overline{44}[/tex]

Therefore, because [tex]-1.35[/tex] is less negative than [tex]-1.\overline{44}[/tex],

[tex]-1.35[/tex] is bigger (larger).