The volume of a cone of radius r and height h is given by V=πr²h³. If the radius and the height both increase at a constant rate of 12 cms/sec, at what rate, in cubic centimeters per second, is the volume increasing when the height is 9 centimeters and the radius is 6 centimeters?

Answer:

(24*10)+50=290

Step-by-step explanation:

a) The equation for the amount of money Autumn makes is y = 10x , where x is the number of bracelets she sells and y is the total amount

b) The amount Autumn makes is $ 290

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

a)

Let the number of bracelets Autumn sells be = x

Let the cost of one bracelet be = $ 10

Now , the equation will be

So , the cost of x number of bracelets y = number of bracelets x cost of one bracelet

The cost of x number of bracelets y = 10x

So , the equation is y = 10x

b)

The equation is y = 10x

The cost of 5 bracelets = 10 x 5

                                       = $ 50

Now , the cost of 24 bracelets = 24 x 10

                                                  = $ 240

So , the total amount Autumn makes = cost of 5 bracelets + cost of 24 bracelets

The total amount Autumn makes = 240 + 50

                                                       = $ 290

Hence ,

a) The equation for the amount of money Autumn makes is y = 10x , where x is the number of bracelets she sells and y is the total amount

b) The amount Autumn makes is $ 290

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Answer:

The distance from the ground to the top of the ladder the building is touched is 16 feet.

Step-by-step explanation:

Given:

A ladder that is 20 feet tall is leaning against a building.Samuel measures that the base of the ladder touches the ground 12 feet from the base of the building.

Now, to find the distance from base of the building to the top of the ladder where building is touched.

Here, to understand the situation below is the figure attached:

Now, to get the distance from the ground to the top of the ladder where the building is touched we use pythagorean theorem:

[tex]AB^2+BC^2=AC^2\\\\AB^2+12^2=20^2\\\\AB^2+144=400\\\\Subtracting\ both\ sides\ by\ 144\ we\ get:\\\\AB^2=256\\\\Using\ square\ root\ on\ both\ sides\ we\ get:\\\\AB=16\ feet.[/tex]

Therefore, the distance from the ground to the top of the ladder the building is touched is 16 feet.

Answer:

The correct option is;

d. 24.2 to 25.6

Step-by-step explanation:

Here we have a sample with unknown population standard deviation, we therefore apply the student t distribution at 64 - 1 degrees of freedom

Therefore, we have

[tex]CI=\bar{x}\pm t\frac{s}{\sqrt{n}}[/tex]

Where:

[tex]\bar x[/tex] = Mean = 25

σ = Standard deviation = 2

n = Sample size = 64

t = T value at 98% = [tex]\pm 2.387[/tex]

Which gives

[tex]CI=25\pm t_{63}\frac{2}{\sqrt{64}}[/tex]

That is the value is from

24.40325 to 25.59675 which gives,by rounding to one decimal place, is

24.4 to 25.6.

The 98% confidence interval for the true average age of all students at the university, given a sample mean age of 25, standard deviation of 2, and a sample size of 64, is approximately option (d) 24.4 to 25.6 years.

The 98% confidence interval for the true average age of all students in the university can be calculated using the sample mean, the sample standard deviation, and the size of the sample. Since the population standard deviation is unknown and the sample size is less than 30, we use the t-distribution to find the critical value (t).

First, we find the t-score corresponding to a 98% confidence level with 63 degrees of freedom (n-1 = 64-1). Using a t-distribution table or calculator, the t-score is approximately 2.390.

Next, we calculate the margin of error (ME) using the formula:
ME = t * (s/√n)
where s is the sample standard deviation and n is the sample size. Plugging in our numbers:
ME = 2.390 * (2/√64) = 0.5975

Finally, we add and subtract this margin of error from the sample mean to find the confidence interval:
CI = mean ± ME
CI = 25 ± 0.5975
CI = (25 - 0.5975, 25 + 0.5975)
CI = (24.4025, 25.5975)

Therefore, the 98% confidence interval for the true average age is approximately 24.4 to 25.6 years.

Answer:

If you're asking about which graph would be better, you can show it by a histogram best.

Step-by-step explanation:

Sorry if this is not your question if not I misunderstood, but a line graph is to measure the changes between data, while histograms measure a single measurement for each subject matter. So the best graph to display this info would be through a histogram

Answer:

The x-intercepts would be where the line hits the x-axis, so the x-intercepts would be:

-3, 2, and 5.

Step-by-step explanation:

Answer:

q4 is -3,2,5

and for q3 is the start point

Answer:

a. probability, when the null hypothesis is true, of obtaining a sample result that is at least as unlikely as what is observed

Step-by-step explanation:

In Statistics, a p-value also known as the probability value is the probability, when the null hypothesis is true, of obtaining a sample result that is at least as unlikely as what is observed.

The p-values can be calculated by using spreadsheets, statistical software and p-value tables and is widely used in research fields such as economics, physics, sociology, accounting etc.

The p-value can be mathematically expressed as a function of the null hypothesis, H and the random variable, X.

In response to the question, we may say that As a result, the can expression contains 72 tablespoons of pineapple juice.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

To begin, we must convert the provided measurements to the same unit.

2 tablespoons = 1 fluid ounce

3 teaspoons = 1 tablespoon

Thus, 12 fluid ounces of canned pineapple juice equals:

12 fluid ounces divided by 2 tablespoons per fluid ounce is 24 tablespoons

And because we need to know how much juice is in teaspoons, we can convert tablespoons to teaspoons by:

72 teaspoons = 24 tablespoons × 3 teaspoons/tablespoon

As a result, the can contains 72 tablespoons of pineapple juice.

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Answer:

C. d = 10t + 10

Step-by-step explanation:

If d represents the distance, you know that the equation on the other side has to have +10 included in it because this was stated in the problem (he has traveled 10 miles). C is the only option with +10, but if you'd like a further explanation on the 10t part... by the end of his trip, he has traveled 30 miles total.  Subtract the 10 he initially traveled before arriving at the gas station, and he has traveled 20 miles in two hours. 20 (miles) / 2 (hours) = 10, so after the gas station, he traveled at an average speed of 10 mph. We now know that he traveled 10 miles, plus another 10 miles for every additional hour (t) he travels after that. This gives us d = 10t + 10.

Answer:

Step-by-step explanation:

Given

Volume of Cylinder (V)= 480 cm

height (h) = 30 cm

radius (r) = ?

WE KNOW THAT WE HAVE FORMULA

Volume (V) = [tex]\pi r^{2} h[/tex]

           480 = 3.14 * r^2 *30

            480 = 94.2 r^2

             480/94.2 = r^2

               r^2 = 5.1

                 r =[tex]\sqrt{5.1}[/tex]

Therefore r = 2.3 cm

Answer:

-6 and 4

Step-by-step explanation:

the explanation is in the picture

please like and Mark as brainliest

Answer:

y = x + 2

Step-by-step explanation:

It looks like its adding 2 everytime.

y = x + 2

Hi there! Hopefully this helps!

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Answer: The population is 1,625.

So the equation is:

p = 35t + 1,450.

t = the number of years since 2015.

2020 - 2015 = 5.

So now we are in 2020, which is 5 years ahead from 2015.

So: t = 5.

Now we need to rewrite the equation, then evaluate.

35(5) + 1,450 =

175 + 1,450 =

Answer:

X = 76*4

= 304 cups of food

Step-by-step explanation:

Given:

So Let X is the number of cups of food that elephants eat per day, we have the equation:

X = 76*4

= 304 cups of food

Hope it will find you well.

Answer:

The answer is 5, 10, 15, 20 or any positive multiples of 5

Step-by-step explanation:

Since the ratio of green grapes to the total number of grapes is 9:14 and there are only purple and green grapes on the shelf. It implies the total number of purple grapes to overall grapes is 5:14.

Since this ratio is already at it's lowest form, it implies the possible number of purple grapes are 5, 10, 15, 20 or any positive multiple of 5.

Final answer:

To find the total daily water usage of the family, divide the amount of water they use for cleaning, 68.9 gallons, by the percentage of their total usage that goes to cleaning, which is 26.5%. The result is that the family uses about 260 gallons of water every day.

Explanation:

To calculate how many gallons of water the family uses every day, we need to establish the total daily water usage based on the percentage used for cleaning.

Since we know that 26.5% of their total water usage is allocated for cleaning, and they use 68.9 gallons for this purpose, we can find the total daily usage with a simple division:

Total daily water usage = Water used for cleaning / Percentage used for cleaning Total daily water usage = 68.9 gallons / 0.265 Total daily water usage = 260 gallons (rounded to the nearest whole number)

Thus, the family uses approximately 260 gallons of water per day for all their needs, including cooking, cleaning, and drinking.

Final answer:

To find out how many gallons a family uses every day, set up a proportion to find the total amount of water used for cleaning and solve for x. The family uses approximately 259.62 gallons of water every day.

Explanation:

To find out how many gallons a family uses every day, we need to determine the total amount of water used for cleaning. The question states that 26.5% of the water used each day is for cleaning, and the family uses 68.9 gallons for cleaning. We can set up a proportion to find the total amount of water used:

26.5% / 100% = 68.9 / x

Now we can solve for x by cross multiplying:

26.5x = 68.9 * 100

Dividing both sides of the equation by 26.5, we find that x is approximately 259.62.

Therefore, the family uses approximately 259.62 gallons of water every day.

Final answer:

Maura saves $14.10 by purchasing 30 daffodil bulbs in the more economical 3-bulb packages instead of the 2-bulb packages.

Explanation:

To determine how much Maura saves by buying 30 daffodil bulbs at the better price, we first need to calculate the price per bulb for each package option and then find the total cost for 30 bulbs. Let's compare the two package options:

The package of 3 bulbs has a better price per bulb than the package of 2 bulbs. To buy 30 bulbs at the better price, Maura would need 10 packages of 3 bulbs, which will cost:

10 packages × $5.37 per package = $53.70

Now let's calculate how much it would cost if she bought the 2-bulb packages:

Since 30 is an odd number, Maura would need to buy 15 packages of 2 bulbs to get 30 bulbs. This will cost:

15 packages × $4.52 per package = $67.80

Maura saves by purchasing the 30 bulbs in 3-bulb packages:

$67.80 - $53.70 = $14.10

Therefore, Maura saves $14.10 by purchasing the 30 bulbs in the more economical 3-bulb packages.

Answer: 280

Step-by-step explanation:

??/500=7/100

7x500/100

35/500=7/100

35x8=280

I think this is the answer.

Answer:

$859.09

Step-by-step explanation:

Answer:

It's correct answer is A.

Answer:

A represents the connector of X and Y.

Step-by-step explanation:

By interpreting the stem-and-leaf plot, it is found that no zoos have exactly 17 sloths.

In the stem-and-leaf plot, we locate the stem which corresponds to the number '1', and then we check the corresponding leaves. In this case, the appropriate stem is '1' and the leaves under this stem correspond to the tens place of the number of sloths. So, now we check the leaf '7' under stem '1'. Seeing the 7 in the ones place next to the stem of 1, we find that there is no such instance in the plot. Therefore, we can conclude that no zoos have exactly 17 sloths.

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Stem-and-leaf plots represent numerical data in statistics. The analysis of the provided stem-and-leaf plot reveals that 2 zoos have exactly 17 sloths.

Stem-and-leaf plots are used in statistics to represent numerical data. Each observation is divided into a stem (leading digit(s)) and a leaf (final significant digit). In the given plot, if a zoo has exactly 17 sloths, then the stem is 1 and the leaf is 7. By looking at the plot, it can be observed that there are 2 zoos with exactly 17 sloths.

here is the full question- A zookeeper created the following stem-and-leaf plot showing the number of sloths at each major zoo in the country:

0 3

1 6 7 7

2 0 4

3 0 1 1 2 4 7 9 9

4 1 2 3 5 7

Key: 4|1=41 sloths How many zoos have exactly 17 sloths? x=frac =frac (-)²(-)² 2005.

Answer:

1,177.5cm^3 of candle wax will be required.

Step-by-step explanation:

The attached files contain further information so please check them.

Answer:

1 μ = M μ ≠ M 2

2 μ > M μ < M 1

3 μ < M μ > M 1

If we use a 5% significance level, the p-value of 0.165 is not less than α = 0.05 so we would not

reject H0 : pf = pm. T

Answer:

The correct options are 1, 3, and 5

Step-by-step explanation:

Answer:

Hence the function only :

Secx and Cosx functions are symmetric about y-axis

And remaining functions are not symmetric about y-axis.

Step-by-step explanation:

Given:

Six circular function as :

y= sinx ,y=cosx , y=tanx,  y= cotx ,y=secx  y=cosecx

To Find:

Which functions are symmetric about the y-axis

Solution:

The function is said to be symmetric about the y-axis is given by

f(x)=f(-x)

Now

1)For y=sinx  i.e. f(x)=sinx

So put x=-x

f(-x)=sin(-x)

=-sinx

Hence f(x)≠f(-x)

This function is not symmetric about y-axis

2)For y=cosx ,i.e. f(x)=cosx

put  x=-x

f(-x)=cos(-x)...............(as value for x and -x cos value remain the same )

=cosx

hence f(x)=f(-x)

This function is symmetric to the y-axis

3)For y=tanx     i.e   f(x)=tanx

put  x=-x

f(-x)=tan(-x)

=-tanx

Hence f(x)≠f(-x)

This function is not symmetric about y-axis

4)For y=cotx  i.e.  f(x)=cotx

Using above observation,

f(x)≠f(-x)

This is not symmetric about y-axis

5)For y=secx  i.e f(x)=secx

f(x)=f(-x)

This function is symmetric about y-axis.

6) for y=cosecx

f(x)≠f(-x)

This function is not symmetric about y-axis

Given:

In the given triangle,

With respect to y, Perpendicular = 10 cm and Base = 8 cm

To find the value of y.

Formula

By Trigonometric Ratio we get,

[tex]tan\theta = \frac{Perpendicular}{Base}[/tex]

Now,

Putting the values of perpendicular and base we get,

[tex]tan\theta = \frac{10}{8}[/tex]

or, [tex]\theta = tan^{-1} (\frac{10}{8})[/tex]

or, [tex]\theta = 51.34 ^\circ[/tex]

Rounding off to the nearest tenth, we have;

[tex]\theta = 51.3 ^\circ[/tex]

Hence,

The value of y is 51.3°.

Answer:

Step-by-step explanation:LOOK IN PG 1 OF PDF 3 QUESTION.

HOPES THIS WAS HELPFUL

The required probability is 9/23

According to the problem,

Number of students with experience and a degree = ( 140 - 10 ) = 130

Number of students with only degree = (220 - 130) = 90

Probability that a new hire has a college degree but no experience              = 90/230 = 9/23

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Answer:

(-∞,∞)

B) x cannot equal -4, 2

Step-by-step Explanation:

The function, y = x + 2, has a domain of (-∞,∞) because the equation will remain true no matter number you plug for x.

For the second question, x would be equal to -2 and 4.  You can find this by factoring the equation.  x² + 2x - 8 = (x - 2)(x + 4)  Your answer should be B

Answer:

B) x cannot equal −4, 2

Step-by-step explanation:

x² + 2x - 8 = 0

When x = -4, 2

When the denominator becomes zero, function becomes undefined

Answer:

$38.92

Step-by-step explanation:

In this question, we are calculating the amount it would cost purchasing a turkey wing after giving some rebate.

Firstly, we calculate the cost of purchasing 22 pounds turkey

That would be 22 * $1.79 = $39.38

Now we subtract the cost of the rebate ;

That would be $39.38 -$1 = $38.38

Now, we add the envelope cost and the stamp cost

That would be $38.38 + $0.39 + $0.15 = $38.92

The final cost of the 22-pound turkey after accounting for the price per pound, mail-in rebate, and the costs of an envelope and stamp is $38.92.

The cost of a 22-pound turkey at $1.79 per pound is calculated first, then subtract the $1 mail-in rebate, and finally add the costs of the envelope and the stamp required for the rebate.

First, find the total cost of the turkey without the rebate:

Next, add the cost of the envelope and stamp:

After receiving the rebate of $1, the final cost is calculated:

Therefore, the final cost of the turkey after the rebate is $38.92.

Answer:

In that day 1300 children and 700 adults were admitted.

Step-by-step explanation:

Since the people who enter the park are either adults or children, the sum of these two types of people must be equal to the total amount that entered the park. So we have:

children + adults = 2000

The total amount collected must be the sum of the people that entered the park multiplied by the ticket fee for each type. We have:

1.5*children + 4*adults = 4750

We now have two equations and two variables so we can solve the system.

children + adults = 2000                                             equation 1

1.5*children + 4*adults = 4750                                     equation 2

We can multiply the equation 1 by -1.5 and sum it with the equation 2 to solve for adults, we have:

-1.5*children - 1.5*adults = -3500

1.5*children + 4*adults = 4750

2.5*adults = 1750

adults = 1750/2.5 = 700

To solve for children we apply the found value for adults on the equation 1.

children + 700 = 2000

children = 2000 - 700 = 1300

In that day 1300 children and 700 adults were admitted.

Answer:

700 adults and 1300 children

Step-by-step explanation:

Let 'C' represent number of children

'A' represent number of adults

->If  2,000 people entered the park, the equation will be

C+A=2000

C=2000-A ->eq(1)

->$1.50 for children and $4.00 for adults.

$1.50C+$4.00A=$4,750

Substituting for C from above.

$1.50(2000-A)+$4.00A= $4,750

$3000-$1.50A+$4.00A=$4,750

$2.50A = $4,750 - $3000

$2.50A=$1750

A= 700

and for children:

eq(1)=>

C=2000-700

C= 1300

Thus, 700 adults and 1300 children were admitted.

Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Given:

Skylar has 1/2 of her sub left from lunch she wants to cut it into thirds

Question asked:

Find the length of each piece ?

Solution:

Sub left from lunch = [tex]\frac{1}{2}[/tex]

As she want to cut into third, we will divide [tex]\frac{1}{2}[/tex] into [tex]\frac{1}{3}[/tex]

[tex]=\frac{1}{2}\div\frac{1}{3}\\ \\ =\frac{1}{2}\times\frac{3}{1} \\ \\ =\frac{3}{2}[/tex]

Thus, length of each piece will be [tex]\frac{3}{2}[/tex]