A can of diced tomatoes has a height of 11.5 cm and a diameter of 10 cm. What is the volume of the can? Use 3.14 for pie.DO NOT round your answer.

Explanation

The model has the form

Where a=initial amount

y= final amount

K= growth rate constant

t= time

When 140 kg of substance is left after 7 hours, the formula can be remodeled to be.

Therefore, the first solution is

For part b we have 16 hours.

Thus, the answer is 36kg

The confidence interval for the mean score of the 30 randomly selected students is: 99% CI {78.26, 89.73}

Confidence interval is the range of values for which which is expected to have the values at a certain percentage of the times.

Given data form the question

99% confidence interval

30 randomly selected students

mean sample = 84

Standard deviation = 12.2

Definition of variables

confidence level, CI = 99%

mean sample, X = 84

standard deviation, SD = 12.2

Z score, z = 2.576

sample size, n = 30

The formula for the confidence interval is given by

[tex]CI=X+Z\frac{SD}{\sqrt{n} }[/tex]    OR    [tex]CI=X-Z\frac{SD}{\sqrt{n} }[/tex]  

[tex]=84+2.576\frac{12.2}{\sqrt{30} }[/tex]

=[tex]=84+2.576*2.2274[/tex]

= 84 + 5.7378     OR       84 - 5.7378

= 89.7378           OR        78.2622

=  89.73 to 78.26  

The confidence interval for the mean score of all students is 78.26 to 89.78

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Answer: 2

Step-by-step explanation: 0.300 0.375 0.325 1.000 = 2

To solve the problem, we will define a function that given the weight of the package, will determine the cost of the mailing. Let x be the weigth of the package in oz and let f(x) be the cost of mailing the package. We are told that if the weight is less than 4, then the rate is 1.50. So, in math notation that would be f(x) = 1.50 if x<4. Now, we are told that if the package weights between 4 and less than 8, then the rate is 2.50. So, that is f(x) = 2.50 if 4<=x<8. Finally, we are told that if the package weights between 8 and 12, the cost is 3.50. So f(x) = 3.50 if 8<=x<=12. So the final math expression for f(x) is

1.50 if x<4

f(x) = 2.50 if 4<=x<8

3.50 if 8<=x<=12.

Given the following question:

Your answers are the first and second options.

5 to 6 odds means that, out of 11 possible outcomes, odds are that there will be 5 of one kind of outcome and 6 of another kind of outcome.

In this case, you are given 5 to 6 odds, which means that out of 11 possible outcomes you will win a bet 5 times, and lose it 6.

In fraction, it will look like this:

Because of that, the probability of winning the bet is 45.45%, and in a fraction, it is 5/11, which means you will win in 5 out of 11 scenarios.

Given the fucntion:

f(x) = tanx

Let's graph the function and input the correct values in the box.

• To find the y-intercept of the function, input 0 for x and solve:

Therefore, the y-intercept is:

(0, 0)

• The period of the function:

The fundamental period of a tangent function is π.

Now, let's find points on the graph:

Therefore, the points are:

ANSWER:

The tangent function's period is π . The y-intercept of the function is (0, 0).

The points are:

The parabola that has the height and width similar to the Gateway arc, gives;

(a) The quadratic equation of the parabola is presented as follows;

[tex] f(x) = -6.991 \times 10^{-3} \cdot x^2 + 4.181 \cdot [/tex]

(b) The completed table is presented as follows;

Width. Height

567. 63.12

478. 225.67

308. 459.2

The shape of a quadratic function is a parabola, which is either upward facing or downward facing

(a) The given dimensions of the arc are;

Height = 625

Width at the base = 598

The points on the parabola are therefore;

(0, 0), (598÷2, 625) = (299, 625), (598, 0)

The equation of the parabola is of the form;

f(x) = a•x² + b•x + c, which gives;

f(0) = 0 = a×0² + b×0 + c = c

c = 0

f(299) = 625 = a×299² + b×299 + 0...(1)

f(598) = 0 = a×598² + b×598...(2

(a×598² + b×598) - 2×(a×299² + b×299) = 0 - 2×625

a•178802 = -2×625

a = -2×625 ÷ 178802

a ≈ -6.991 × 10^(-3)

b ≈ 4.181.

The equation is therefore;

[tex] f(x) = -6.991 \times 10^{-3} \cdot x^2 + 4.181 \cdot [/tex]

(b)

The table of values is completed as follows;

When the width is 567 feet, x = 299 - 567÷2 = 15.5

[tex] \displaystyle{f(15.5) = -6.991 × 10^{-3} \times 15.5² + 4.181 \times 15.5 approx 63.12} [/tex]

When the width is 478 feet, x = 299 - 478÷2 = 60

[tex] \displaystyle{f(60) = -6.991 × 10^{-3} \times 60² + 4.181 \times 60 approx 225.67} [/tex]

When the width is 308 feet, x = 299 - 308÷2 = 145

[tex] \displaystyle{f(145) = -6.991 × 10^{-3} \times 145² + 4.181 \times 145 approx 459.2} [/tex]

The table is therefore presented as follows;

Width. Height

567. 63.12

478. 225.67

308. 459.2

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To find the amount of servings, we just need to divide the entire bar weight by the serving weight. Solving this calculation, we have

Answer:

To isolate the variable, we have to add 3 to both sides of the equation to keep the equation balanced.

So x = 10

Explanation:

Given the below equation;

To isolate the variable, we have to add 3 to both sides of the equation to keep the equation balanced;

The statement "If I am not in San Juan, then I am not in Puerto Rico." is the inverse and contrapositive statement because it is inverse of "If I am in San Juan, then I am in Puerto Rico."

The inverse function of a function f in mathematics is a function that reverses the operation of f. If and only if f is bijective, then the inverse of f is true. A function that "undoes" another function is called an inverse. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹.

When you reverse the hypothesis and the conclusion in a statement and reject both of them, you have a contrapositive statement. When the hypothesis and the conclusion are switched in this example and both are negated, the outcome is: If it is not a triangle, then it is not a polygon.

Here,

The statement is "If I am in San Juan, then I am in Puerto Rico."

So the contrapositive and inverse will be:

"If I am not in San Juan, then I am not in Puerto Rico."

Because it is the opposite of "If I am in San Juan, then I am in Puerto Rico," the statement "If I am not in San Juan, then I am not in Puerto Rico" is the inverse and contrapositive statement.

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ANSWER

88

EXPLANATION

Let x be the miles driven and y be the earnings of the company when they drive for x miles.

If the company charges $0.17 per mile driven plus a flat rate of $85, then the total cost for moving x miles away is,

Now, we have to find for how many miles, x, the company must drive to earn $100 or more,

Subtract 85 from both sides,

And divide both sides by 0.17,

Hence, the company must drive for at least 88 miles to earn at least $100, rounded to the nearest mile.

The range of the following function is

We can also call the range of a function an image, the range or image of a function is a set, we can see this set looking at the graph and see which values of y the function have, remember that we can have the same y value for different x value, looking at our graph we can see that this function comes from high y values, have a vertex on (3,1), in other words, it stops at y = 1 and then start growing again, and go on repeated values of y, then we can say that the image (values of y that the function assumes) is all values bigger than 1, therefore {y > 1}.

hello

the car travels 273 miles in 6 hours, how many hours will it take to travel 378 miles.

let the number of unknown hours be represented by x

the car spent approximately 8.31 hours to travel a distance of 378 miles

50 + 10m = 90 Reason: This is a right angle, which sum up to 90 degree.

10m = 90 - 50

10m = 40

m = 40/10

m = 4

We can find the maximum value by creating a list of the provided numbers from the smallest to the largest.

As we see on the list, the last number and the largest is 41. Some tools are used to solve this kind of problem like the diagram of leaves and stems, a table os fre

Given the information about the triangle, we can use the cosine function on angle x to get the following:

solving for x, we get:

therefore, the value of x is 61.1

Amount deposited = $8500

Rate = 5%

time for interest = 6years

Compounded semiannually

The formula for semiannually is

From the given information

P = $8500

r = 5

t = 6

Since the investment was compounded semiannually then

n = 2

Substitute the values into the formula

This gives

Solve for A

To find the interest

Recall

Where I, is the interest

Hence

c.

The line equation is of the form

From the graph, we observe and find these points

(1,5) and (0,4) lie on the given line.

Substituting x=1, y=5 in equation (1), we get

Substituting x=0, y=4 in equation (1), we get

Substituting c=4 in equation (2), we get

Substituting c=4,m=1 in equation (1), we get

We need to write this equation in the form of r(x) = p(x) / q(x).

Let r(x)=x+5, q(x)=x, and subsitute in the equation , we get

Using the cross-product method, we get

Substitute values in equation (3), we get

Hence the required equation is

Recall that if two lines have the same slop then these two lines are parallel to each other.

the y-intercept is an x-coordinate of the point where the line intersects at the y-axis.

Consider graph 1.

The line intersects at one point and has different slopes, hence this has one solution.

(A) and (H) is true for graph 1.

Consider graph 2.

The lines have the same slope, therefore parallel but there is no y-intercept point.

This have infinitely many solutions.

They are also the same line.

(E) and (F) is true for this graph 2.

Consider graph 3.

The lines have the same slope and they are parallel.

It gives B) is correct

They do not intersect since parallel does not intersect each other.

It gives C) is correct

There is no solution since they do not intersect.

It gives G) is correct.

These lines have intercepted at -1 and -4.

It gives D) is correct

B), D), C), G), D) are correct for graph 3.

Results:

Options Graph

A) 1

B) 3

C) 3

D) 3

E) 2

F) 2

G) 3

H) 1

In this problem

the vertex is given ------> (40/2,12)-------> (20,12)

The first intercept is (0,0)

therefore

second intercept is

x-intercept=20+20=40

(40,0) is the coordinates of the second x-intercept

(the vertex is the midpoint between the first and second x-intercept)

see the attached figure

After 5 minutes there will be 2.29376 quarts of antifreeze in the system.

Given,

The capacity of the cooling system of a car = 20 quarts

The mixture in the system is 7 quarts of antifreeze and 13 quarts of water.

The running rate of water = 1 gal/min

Homogenous mixture also runs 1 gal/min

We have to find the antifreeze in the system at the end of 5 minutes;

Here,

1 quart = 0.25 gallons

7 x 0.25 = 1.75 gallons of antifreeze

13 x 0.25 = 3.25 gallons of water

1 = 0.2 of 5

0.57344 gallons = 2.29376 quarts

After 5 minutes there will be 2.29376 quarts of antifreeze in the system.

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If the figures are similar, the proportion between the corresponding sides is the same.

The side of 30 cm corresponds to the side of 24 cm, and the side of 13 cm corresponds to the side of x cm.

So if the proportion is the same, we have that:

So the value of x is 10.4 cm, therefore the answer is b.

We are given that a total amount is $864, if a deposit of $216 is given, then the total amount to pay is the following:

Therefore, there is $648 to pay.

The equation that will represent this situation will be:

Thus:

If we check in a standard normal table. the z-score that corresponds to a probability of 0.525 is 0.063.

Answer: z-score is 0.063.

P = $1000

r = 4% = 4/100 = 0.04

t = 6 years

Therefore,

Let's solve the following expressions:

a.) 7 - (5t - 13) = -25

Therefore, t = 9

b.) -15b + 21 + 5b = -19

Therefore, b = 4

The smallest degree of rotation is achieved through the division of the full circumference over the total number of sides

The answer would be 3.75°

Given data:

a=9 , b = 10

use the phythagoras theorem,

thus,

and,

we have

C -----> total charge

b -----> number of buckets of balls

Remmeber that

the equation of the line in slope intercept form is equal to

y=mx+b

where

m is the slope and b is the initial value or y-intercept

In this problem

m=$1.50 per buckey

b=$5

therefore

y=1.50x+5

or

C=1.50b+5