a new toothpaste is supposed to keep cavities of children in a certain age group no more than 3 times per year on average (treated as h0). cavities per year for this age group are normal with standard deviation 1. a study of 2500 children who used this toothpaste found an average of 3.05 cavities per child. do these data, at the 1 percent level of significance, contradict the claimed function of the toothpaste?

Solution

For this case we know that one base angle is 67.5º

Then the other base angle is 67.5º

Then we can find the vertex angle like this:

180 - 67.5- 67.5= 45º

Then the answer for this case is:

45º

Answer:

what is the volume of the sphere? use a=3.14 and round your answer to the nearest hundredth. the sphere is 3 inches? V = 113.1

Step-by-step explanation:

V=4/3πr3=4/3·π·3*3≈113.09734

So your volume is = 113.1

The height of the shorter flagpole is 22.5 feet, given that the taller 30-foot flagpole casts a shadow of 20 feet and the shorter flagpole casts a shadow of 15 feet.

We have two flagpoles, a taller one and a shorter one. We are given the following information:

The taller flagpole is 30 feet tall, the taller flagpole casts a shadow of 20 feet, the shorter flagpole casts a shadow of 15 feet.

We want to find the height of the shorter flagpole, denoted as "h."

We can use the concept of similar triangles to solve this problem. Similar triangles have the same shape but can be different in size. In this case, the two flagpoles and their shadows form similar triangles.

Let's set up a proportion using the heights and shadows of the flagpoles: h / 15 = 30 / 20.

We know that the ratio of corresponding sides in similar triangles is equal. In this case, the ratio of the heights of the flagpoles is equal to the ratio of their shadows.

Now, we can solve the proportion to find the height of the shorter flagpole (h): h = (15 * 30) / 20

Simplifying the equation: h = 450 / 20

h = 22.5 feet. Therefore, the height of the shorter flagpole is 22.5 feet.

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The ratio of junior to adult = 6/5

What is proportion?

An equality between two ratios. According to proportion, if 2 sets of given numbers area unit increasing or decreasing within the same quantitative relation, then the ratios area unit aforesaid to be directly proportional to every different.

Main body:

Given - data in the question

To find answer the question

Solution - Let no of junior, children and adults be x, y, z respectively.

Now, ratio of junior to children = 1/3

So, x = 3y

Ratio of children to adult = 5/2

So, 5y = 2z

.(2)

So, from (1) we get, y = x / 3

So, 5x / 3 = 2z

⇒5x = 6z

⇒ x/z=6/5

Hence, the ratio of junior to adult = 6/5

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Answer:

-13

Step-by-step explanation:

−2+3(1−4)−2

=−2+(3)(−3)−2

=−2+−9−2

=−11−2

=−13

Step-by-step explanation:

Is this ok

If its correct, please don't forget to like and mark me

The measure of angle A remains as (4x + 20) degrees until we have more information or the specific value of x.

The measure of angle A is given by the expression (4x + 20) degrees. To find the specific measure of angle A, we need to determine the value of x or be provided with additional information.

The given information provides the measure of angle D as (5x - 65) degrees, but it does not directly give us the measure of angle A.

Without knowing the value of x or having any additional information, we cannot determine the specific measure of angle A.

The expression (4x + 20) represents the general form of the measure of angle A, but we need more information or the value of x to evaluate it.

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Answer:

The answer is "Do her friends have accounts at the same bank?"

Step-by-step explanation:

In this question, the above given-choice is correct because the account on the same bank has certainly, but when a retirement fund in a company is concerned, you could only have a savings account on their behalf, and the mutual funds must then be distributed, and these several savings accounts can be opened is by tracking the amount they need to save for every savings target.

Answer:

depends on the other side, so... maybe

Step-by-step explanation:

If you have a rectangle and you know one side is 5.25, then if the perpendicular side looks about the same length or longer, then the area of the rectangle is at least 25.

Imagine you have a rectangle with a known base of 5.25, then if the rectangle is at least as tall as it is wide, then the area is over 25.  If the rectangle is very close to a square then the area should be near 25, and if the rectangle is visually shorter than it is wide then the area is less than 25

Answer:

Step-by-step explanation:

this is a simultaneous equation question

f(1)=8  so  a(1) + b = 8

f(4)=17 so a(4) + b = 17

can you figure this out from here ???

if you can't below is how to solve it

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a + b = 8

4a+b=17

multiply the top equation by 4 and then subtract the bottom one from the top

4a+4b = 32

-(4a +b = 17)

3b = 15

b=5

now plug 5 into the first equation

a + 5 = 8

a=3

there you go :)

The relationship between CE and AD is that, AD is one-fourth the length of CE

From the Circle given :

CD is half the length of CE

AD is half the length of CD

Combining the relationships,

Therefore, the correct option is B.

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Answer:

3/11

Step-by-step explanation:pls mark me brainliest

Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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Answer:

14 pints are  in 28 cups

Step-by-step explanation:

Answer:

14 pints in 28 cup

Step-by-step explanation:

The value of limit, \(L = \lim_{n→∞} |\frac{ a_{n+1} }{a_n}| \\ \) < 1, for a series \( \sum_{n= 1}^{\infty}a_n \\ \), where \(a_n = \frac{ ( 6n + 7)8^{n+4} }{11^n}\), then by ratio test says series is absolutely convergent. So, option(a) is true.

Ratio test is one of that is used to determine the convergence or divergence of infinite series. It states that \(L = \lim_{n→∞} |\frac{ a_{n+1} }{a_n}| \\ \)

We have a series, \( \sum_{n= 1}^{\infty}a_n \\ \), where \(a_n = \frac{ ( 6n + 7)8^{n+4} }{11^n}\). We have to check the convergence of above series with the help of ratio test. Here, \(a_n = \frac{ (6n + 7)8^{n+4} }{11^n}\).

\(a_{n+1} = \frac{(6(n+1)+ 7)8^{n + 1+4 }}{11^{n+1}}\)

\(= \frac{(6n+ 13)8^{n + 5}}{11^{n+1}}\).

Now, \(L = \lim_{n→∞} |\frac{ a_{n+1} }{a_n}| \\ \)

\( = \lim_{n→∞} |\frac{\frac{(6n+ 13)8^{n + 5}}{11^{n+1}}}{\frac{(6n +7 )8^{n +4 }}{11^{n}}}|\\ \)

\( = \lim_{n→∞} |\frac{(6n+ 13)8^{n + 5}}{11^{n+1}}×\frac{11^{n}}{(6n +7 )8^{n +4 }}|\\ \)

\( = \frac{8}{11}\lim_{n→∞} |\frac{6n+ 13}{6n+7 }|\\ \)

\( = \frac{8}{11}\lim_{n→∞} |\frac{n(6+ \frac{ 13}{n})}{n(6 +\frac{7}{n} )}|\\ \)

\( = \frac{8}{11} = 0.72 \) < 1

=> L < 1 , so, from ratio test ∑an converges absolutely. Hence, series is convergent.

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Complete question:

consider the series \( \sum_{n= 1}^{\infty}a_n \\ \), where \(a_n = \frac{ ( 6n + 7)8^n }{11^n}\)

in this problem you must attempt to use the ratio test to decide whether the series converges

compute

\(L = \lim_{n→∞} |\frac{ a_{n+1} }{a_n}| \\ \)

enter the numerical value of the limit if it converges, inf if the limit for diverges to infinity, minf if it diverges to negative infinity, or div if it diverges but not to infinity or negative infinity.

which of the following statements is true?

a) the ratio test says that the series converges absolutely

.b) the ratio test says that the series diverges.

c) the ratio test says that the series converges conditionally.

d). the ratio test is inconclusive, but the series converges absolutely by another test or tests.

e) the ratio test is inconclusive, but the series diverges by another test or tests

.f) the ratio test is inconclusive, but the series converges conditionally by another test or tests.

enter the letter for your choice here: ?

Answer:

64°

Step-by-step explanation:

Both triangles represent a right angle by the small box in the angle.

Right angles = 90°

Since the triangles are congruent, then they would have the same measurements in their angles an sides. All triangles also have a sum of 180°. So, we can just subtract (26 + 90) from 180 to get the third angle.

180 - (26 + 90)

180 - 116

64

So, the m∠KLM is 64°.

Arrange the data in ascending order,

The mean is ,

The mean is 98.6.

The median is,

The median is 96.5.u

The mode is the value that appears most often in a set of data values.

The range is determined as the difference between the maximum and minimum value.

Answer:x=30/12

Step-by-step explanation:

Answer:

i got 3 1/2 hours

Step-by-step explanation:

Answer: 1.5 or 5

Step-by-step explanation:

You have to add 1/4 and 3/4 and I mean you do 3+1=4 then add 4+1=5

Or you can add 1/4+3/4 which is 4/8 then do 4/8+1 whole that equals 1.5

But try both steps and see which one you like best

Answer:

60

Step-by-step explanation:

all angles in an equilateral triangle equal 60 because 180 ÷ 3 = 60

Answer:

60 degrees

Step-by-step explanation:

each angle in a triangle adds up to 180 so 180/3 equals 60

Based on the vacation days that Lisa got when she first started her current job, the equation that models the relationship between the number of years worked and paid vacation days is y = 3x + 2

The number of paid vacation days to Lisa increases by 3 days every year. This is in addition to the 2 days that Lisa got when she first started the job.

The relationship between the vacation days and the number of years worked is therefore:

Number of paid vacation days = Number of years x Increase in paid vacation days annually + Number of paid vacation days when job started

y = 3x + 2

Full question is:

When Lisa started at her current job, her employer gave her two days of paid vacation time with a promise of three additional paid vacation days for each year she remains with the company to a maximum of four work weeks of paid vacation time.

Let x represent the number of years she has worked for this employer and y represent the number of paid vacation days she has earned. Write an equation that models the relationship between these two variables.

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Therefore , the solution of the given problem of factorization comes out to be x=0 and x=1/3.

The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.

Here,

Given:

thus . We do factorization of given expression and

we come on a result

=>  3x - 9x²

=> 3x (1 -3x)

x=0 and x=1/3

Therefore , the solution of the given problem of factorization comes out to be x=0 and x=1/3.

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The true statements regarding the plot of normal distributions A and B are B has the larger mean, and B has the larger standard deviation; options 2 and 3.

A plot of a normal distribution is a bell-shaped curve that represents the probability distribution of a continuous random variable that follows a normal distribution.

The plot shows the frequency of occurrence of values of the variable, with the most common values near the mean and the less common values near the tails of the distribution.

The normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). The mean determines the location of the center of the distribution, while the standard deviation determines the spread or width of the distribution.

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Answer: - 1/3

Step-by-step explanation:

To solve this algebraic expression, you will need to evaluate the equation like this:

13(9x + 3) = 3x + 1

117x + 39 =  3x + 1

117x + 39 - 39 =  3x + 1 - 39

117x = 3x - 38

117x - 3x = 3x - 38 - 3x

114x = -38

 x =  - 1/3

Therefore, the solution to this equation is -1/3. Hope this helps!

Answer:

y = mx + c

since m = 0

c = 9

Answer: 60

suppose: the width of a rectangle is x (x > 0)

⇒ The length of a rectangle is 4x

because  the area of the rectangle is 144 ft

=> 4x.x = 144

⇔ x² = 144/4 = 36

⇒ x = 6

with x = 6 ⇒ The length of a rectangle is 4.6 = 24

the perimeter of the rectangle is (6 + 24).2 = 60

Step-by-step explanation:

Answer:

4 hours to paint all 4 of walls

Step-by-step explanation:

well is it takes her 20 minutes to paint 1/3 of a wall and there is 4 walls to 1/3 on each it would take her 20 minutes for 1/12(total of 4 walls) you would do 20x12 which is 240 then divided by 60 which is 4 so the answer is 4.

The target variable in a classification model should be a categorical variable.

In a classification model, the target variable represents the class or category to which an observation belongs. It is a categorical variable because it assigns each observation to a specific group or class rather than representing a continuous or numerical value. The goal of a classification model is to predict or classify new observations into one of the predefined categories based on their features or attributes. Therefore, the target variable in a classification model should be categorical to facilitate the classification process.

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Answer:

Step-by-step explanation:

perimeter of rectangle=2(length+width)

=2(70+65)

=2*135

=270 feet

Note: Your function is missing some information. It seems your function is

\(f\left(x\right)=\frac{-3}{x}+7\).

So, I am solving the question based on the function \(f\left(x\right)=\frac{-3}{x}+7\),  because it would still solve your query.

Answer:

Please see the explanation.

Step-by-step explanation:

Given the function

\(f\left(x\right)=\frac{-3}{x}+7\)

A function g is the inverse of a function f for y = f(x), x=g(y)

\(y=\frac{-3}{x}+7\)

Replace x with y

\(x=\frac{-3}{y}+7\)

solve for y

\(y=-\frac{3}{x-7}\)

so the inverse of \(f\left(x\right)=\frac{-3}{x}+7\) will be:

\(f^{-1}\:\left(x\right)=-\frac{3}{x-7}\)

Finding the domain of \(f^{-1}\:\left(x\right)=-\frac{3}{x-7}\)

As we know that domain is the set of the possible input values where the function is defined.

so the function domain must be: \(x<7\quad \mathrm{or}\quad \:x>7\)

Therefore,

\(\mathrm{Domain\:of\:}\:-\frac{3}{x-7}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x<7\quad \mathrm{or}\quad \:x>7\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:7\right)\cup \left(7,\:\infty \:\right)\end{bmatrix}\)

See attachment for guidance