Can you please help me this is 6th grade stuff

Answer:

45.8 inches

Step-by-step explanation:

Considering the given dimensions and taking 40 inches for length, 20 inches for height and 10 inches for width. The diagonal that runs from bottom to top of box will give the longest possible length of a pole.

Diagonal at the bottom of box

Diagonal=√(l²+w²)

Where l and w represent length and width respectively

Diagonal=√(40²+10²)=√1700

Diagonal between the height and bottom diagonal

Longest diagonal=√(20²+√1700)=√2100=45.8257569495584

Rounded off, the diagonal is approximately 45.8 inches

The longest length of a support pole that will fit into the box measures approximately 45.8 inches.

To find the longest length of a support pole that will fit into the box, we need to determine the length of the diagonal of the box. The diagonal length can be found using the formula:

diagonal = √(length^2 + width^2 + height^2)

Substituting the given values:

diagonal = √(10^2 + 20^2 + 40^2) = √(100 + 400 + 1600) = √2100 ≈ 45.82 inches.

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Answer:

(27,2)

Step-by-step explanation:

Multiply the x value by 3 to get the transformation

If a function f(x) goes through the point (9,2), the function f(3x) will go through the point (3,2) after substituting x with 3x in the original function.

If the function f(x) passes through the point (9,2), then to determine the corresponding point that f(3x) goes through, we must substitute x with 3x in the original function.

Since we know that f(9) = 2, to find f(3x) we look for a value of x that when multiplied by 3 gives us 9.

That value is x = 3.

Therefore, f(3×3) = f(9) = 2, meaning f(3x) will go through the point (3,2).

Answer:

Correct answer:  x = - 3  and y = - 5

Step-by-step explanation:

Given:

2 x - y = - 1

3 x - 2 y = 1

We will multiply first equation with number (- 2) and get:

- 4 x + 2 y = 2

then we add this equation to another and get:

- 4 x + 3 x = 2 + 1

- x = 3 / · (- 1)

x = - 3

now we replace x = - 3  in the first equation and get:

2 (- 3) - y = - 1  ⇒ - 6 - y = - 1 / ·(- 1)  ⇒ 6 + y = 1  y = 1 - 6 = - 5

y =- 5

God is with you!!!

Answer:

x= -3

y= -5

Step-by-step explanation:

-2 (2x-y= -1) = -4x + 2y = 2

-4x + 2y = 2

3x - 2y = 1

-------------------

-x = 3

x = -3

plug the x= -3 into the equation to find y

The possible y-intercepts for the given continuous function from the table are (0,1) and (0,5).

In this mathematical problem, the student is asking about the y-intercept of a function represented in a table. The y-intercept of a continuous function is a point where the line of the function intersects or touches the y-axis on a graph. This point is always (0, y). If we look at the given points, only (0,1) and (0,5) can potentially be y-intercepts because they have 0 as their x-coordinate, which is the requirement for a point to be a y-intercept.

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Answer:

B. 0

Step-by-step explanation:

if n is anything but 0 then the answer wouldn't be m it would be for example m - 1 or m + 1

for it to remain m then n must be 0

Explanation:

A cross section of a prism will match the base of the prism when the plane of the section is parallel to the base.

If the polyhedron is not a prism, or the lateral faces are not perpendicular to the base, or the plane of cross section is not parallel to the base, you can get a variety of cross-section shapes.

For example, the cross sections of a cube include ...

  triangle, square, rectangle, trapezoid, general quadrilateral, pentagon, hexagon

Answer: A cross section of a prism will match the base of the prism when the plane of the section is parallel to the base.

If the polyhedron is not a prism, or the lateral faces are not perpendicular to the base, or the plane of cross section is not parallel to the base, you can get a variety of cross-section shapes.

Step-by-step explanation.

Answer:

The wallpaper would cost 1105 $

Answer:

[tex]5.3044992\times 10^{10}[/tex]

Step-by-step explanation:

We are given that a license plate consist of 5 digits and 5 uppercase letters

Digits used=0,1,2,..9

Total number of letters=26

Repetition is not allowed

Total number of odd digits=(1,3,5,7,9)=5

The first place filled by 5

Second place filled by 4

Third place filled by 8

Fourth place filled by 7

Fifth place filled by 6

Sixth place filled by 26

Seventh place filled by 25

Eighth place filled by 24

Ninth place filled by 23

Tenth place filled by 22

Total number of possible  different license plates =[tex]5\times 4\times 8\times 7\times 6\times 26\times 25\times 24\times 23\times 22[/tex]=[tex]5.3044992\times 10^{10}[/tex]

The number of possible license plates, considering the restrictions on the first and second odd digits and no repetition, is 53,144,832,000. This was determined by systematically calculating the choices for each digit and letter and then multiplying them together.

Calculating the Number of Different License Plates

To determine the number of different license plates possible, we need to consider two sections: the digits and the letters. The first and second digits must be odd, and repetition of digits and letters is not permitted.

Step-by-Step Calculation:

→ First digit: Since it must be odd (1, 3, 5, 7, 9), there are 5 choices.

→ Second digit: Also must be odd but different from the first, so there are 4 remaining choices.

→ Third digit: Any digit except the first two, leaving 8 choices.

→ Fourth digit: Any remaining digit, leaving 7 choices.

→ Fifth digit: Any remaining digit, leaving 6 choices.

→ First letter: Any uppercase letter, 26 choices.

→ Second letter: Any remaining uppercase letter, 25 choices.

→ Third letter: Any remaining uppercase letter, 24 choices.

→ Fourth letter: Any remaining uppercase letter, 23 choices.

→ Fifth letter: Any remaining uppercase letter, 22 choices.

→ Multiply these choices together:

5 × 4 × 8 × 7 × 6 × 26 × 25 × 24 × 23 × 22

→ Calculate the total:

5 × 4 × 8 × 7 × 6 = 6720

26 × 25 × 24 × 23 × 22 = 7893600

6720 × 7893600 = 53,144,832,000

Therefore, the number of different license plates possible is 53,144,832,000.

Answer:

[tex]t=\frac{37300-38000}{\frac{1000}{\sqrt{18}}}=-2.970[/tex]  

[tex]p_v =P(t_{17}<-2.97)=0.0043[/tex]  

If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is lower than 38000 at 5% of signficance.  

Step-by-step explanation:

We assume this question: A shipping firm suspects that the mean life of a certain brand of tire used by its trucks is less than 38,000 miles. To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 37,300 miles with a standard deviation of 1000 miles. At α= 0.05, does the test suggest that mean life is less than 38000 miles?  because if is not this one is not appropiate

Data given and notation  

[tex]\bar X=37300[/tex] represent the sample mean    

[tex]s=100[/tex] represent the sample standard deviation for the sample  

[tex]n=18[/tex] sample size  

[tex]\mu_o =7500[/tex] represent the value that we want to test  

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is lower than 38000, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 38000[/tex]  

Alternative hypothesis:[tex]\mu < 38000[/tex]  

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

[tex]t=\frac{37300-38000}{\frac{1000}{\sqrt{18}}}=-2.970[/tex]  

P-value  

The degrees of freedom are given by:

[tex] df = n-1= 18-1=17[/tex]

Since is a left tailed test the p value would be:  

[tex]p_v =P(t_{17}<-2.97)=0.0043[/tex]  

Conclusion  

If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is lower than 38000 at 5% of signficance.  

The shipping firm's hypothesis test determines that the mean lifespan of a particular brand of tires is indeed less than 38,000 miles based on their sample data and the significance level.

The shipping firm is performing a hypothesis test about a population mean, where the suspected value is 38,000 miles. The null hypothesis (H0) would be that the mean life of the tires is equal to 38,000 miles, while the alternative hypothesis (H1) is that the mean life is less than 38,000 miles.

Using the provided sample data, we can calculate the test statistic (z-score), which helps us determine the p-value. The test statistic is given by (Sample Mean - Pop Mean) / (Standard Deviation / sqrt(n)) = (37300 - 38000) / (1000 / sqrt(18)). This gives us a test statistic of -3.1623.

We also know that our α is 0.05 for this problem. Now we find the p-value that is associated with this test statistic. If the p-value is less than our alpha, we reject the null hypothesis. Given our test statistic, we will indeed find a very low p-value, less than 0.05, which means we reject the null hypothesis and conclude the mean lifespan of the tires is less than 38,000 miles.

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Answer:

$40,500  I took a test and this was the answer to the question.

Answer:

$40500

Step-by-step explanation:

Answer:

A) 0.0009765625

B) 0.0060466176

C) 2.7756 x 10^(-17)

Step-by-step explanation:

A) This problem follows a binomial distribution. The number of successes among a fixed number of trials is; n = 10

If a 0 bit and 1 bit are equally likely, then the probability to select in 1 bit is; p = 1/2 = 0.5

Now the definition of binomial probability is given by;

P(K = x) = C(n, k)•p^(k)•(1 - p)^(n - k)

Now, we want the definition of this probability at k = 10.

Thus;

P(x = 10) = C(10,10)•0.5^(10)•(1 - 0.5)^(10 - 10)

P(x = 10) = 0.0009765625

B) here we are given that p = 0.6 while n remains 10 and k = 10

Thus;

P(x = 10) = C(10,10)•0.6^(10)•(1 - 0.6)^(10 - 10)

P(x=10) = 0.0060466176

C) we are given that;

P((x_i) = 1) = 1/(2^(i))

Where i = 1,2,3.....,n

Now, the probability for the different bits is independent, so we can use multiplication rule for independent events which gives;

P(x = 10) = P((x_1) = 1)•P((x_2) = 1)•P((x_3) = 1)••P((x_4) = 1)•P((x_5) = 1)•P((x_6) = 1)•P((x_7) = 1)•P((x_8) = 1)•P((x_9) = 1)•P((x_10) = 1)

This gives;

P(x = 10) = [1/(2^(1))]•[1/(2^(2))]•[1/(2^(3))]•[1/(2^(4))]....•[1/(2^(10))]

This gives;

P(x = 10) = [1/(2^(55))]

P(x = 10) = 2.7756 x 10^(-17)

Final answer:

To find the probability that a randomly generated bit string of length 10 does not contain a 0, we consider each scenario separately. For equally likely 0s and 1s, the probability is (0.5)^10. For a 0.6 probability of 1, the probability is (0.4)^10. For varying probabilities of 1, the probability is calculated by multiplying the probabilities for each position.

Explanation:

To find the probability that a randomly generated bit string of length 10 does not contain a 0, we need to consider each scenario separately.

a) If a 0 bit and a 1 bit are equally likely, then the probability of getting a 0 in any position is 0.5. Since the bits are independent, the probability of not getting a 0 in any of the 10 positions is (0.5)^10 = 0.00097656.

b) If the probability of a bit being a 1 is 0.6, then the probability of getting a 0 in any position is 1 - 0.6 = 0.4. Again, since the bits are independent, the probability of not getting a 0 in any of the 10 positions is (0.4)^10 = 0.00604661.

c) If the i-th bit has a probability of 1/(2^i) of being a 1, then the probability of getting a 0 in the i-th position is 1 - 1/(2^i). Multiplying the probabilities for each position gives us the probability of not getting a 0 in any of the 10 positions.

P(Not getting a 0) = (1 - 1/(2^1))(1 - 1/(2^2))(1 - 1/(2^3))(1 - 1/(2^4))(1 - 1/(2^5))(1 - 1/(2^6))(1 - 1/(2^7))(1 - 1/(2^8))(1 - 1/(2^9))(1 - 1/(2^10)) = 0.00563108.

Answer:

The maximum number of quarters that he could have is 13

Step-by-step explanation:

Let x represent the number of quarters he could have. If he has 10 dimes and has at least 20 coins, then

→ x + 10 >= 20

→ x >= 10    (1)

His coins worth at most $4.25. Also, it is known that 1 dollar is equal to 100 cents, 1 dime is equal to 10 cents and 1 quarter is equal to 25 cents.

→ (x * 25) + (10 * 10)  <= (4.25 * 100)

→ 25x  + 100 <= 425

→ 25x <= 325

→ x <= 13  (2)

If we combine the equation 1 and 2:

10 <= x <= 13

The maximum value of x is 13

Answer:

2.71828

Step-by-step explanation:

In this question, we are asked to give the approximate value of the irrational number e.

We should understand that just like Pi, which is the ratio of the circumference of a circle to the diameter, we have the number called e. It is also a consistent like Pi and has an approximate value of 2.71828.

What does it mean when it is called irrational? it is an irrational number because it doesn’t have an exact fraction which is the ratio of two numbers and thus it has a non-ending list of numbers after the decimal point.

Final answer:

The irrational number e, also known as Euler's number, is approximately 2.71828 when rounded to five decimal places. It is crucial in mathematics, particularly calculus.

Explanation:

The question asks for the approximate value of the irrational number e rounded to five decimal places. The number e is a fundamental constant in mathematics, often referred to as Euler's number, which is approximately equal to 2.71828 when rounded to five decimal places.

This number plays a crucial role in various branches of mathematics, especially in calculus, relating to the rate of growth or decay in natural phenomena.

Answer:

  5

Step-by-step explanation:

There are 3 feet in a yard, so 420 feet is 420/3 = 140 yards.

The total number of yards Edith needs is ...

  65 yd + 580 yd = 645 yd

So, the total number of balls of yarn Edith needs is ...

  (645 yd)/(140 yd/ball) ≈ 4.61 balls

Edith needs to buy 5 balls of yarn to make her projects.

Answer:

A. Cat

B. 8

C. 6 people

Step-by-step explanation:

A. Just by looking at it Cat has the least amount of squares

B. There are 10 full squares in total (including the pieces). 80 people divided by 10 boxes is 8.

C. There is 1/2 and 1/4 more people who picked giraffe more than dogs. 1

1/2 of 8 is 4. 1/4 of 8 is 2. 4+2 = 6.

Answer:

The image attach is  the truth table for the compound statement

Step-by-step explanation:

Answer:

the correct answer is -16

Step-by-step explanation:

I took the test

The solution for the expression 4x³y² at x = -1 and y =2 will be -16.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that the expression is 4x³y². The values of x and y are -1 and 2.

The expression at the values of x and y will be solved as:-

E = 4x³y²

Substitute the values of x = -1 and y = 2.

E = 4x³y²

E = 4 x ( -1)³ x ( 2 )²

E = 4 x -1 x 4

E = -16

The value of the expression at x =-2 and y = 2 will be -16.

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Answer: 9/6 metre

Step-by-step explanation:

From the question, Olivia is cutting a 1 1/2m by 3/4m piece of rectangular paper into two pieces along its diagonal

This will result into two congruent triangular pieces.  

Let us first find the area of each piece by finding the area of the original rectangle and dividing it by two.

The area of a rectangle is given by multiplying the length and the width:

1 1/2 × 3/4

We can change the first fraction to an improper fraction:

(1×2)+1 = 2+1 = 3; this gives us 3/2:

3/2 × 3/4 = 9/8 = 1 1/8

The area of the entire rectangle is 1 1/8 sq. m., or 1.125 sq. m.

Divide this by 2:

9/8 ÷ 2

9/8 × 1/2 = 9/16

The area of each rectangle is 9/16 sq. m., or 0.5625 sq.

Answer:

9/16

Step-by-step explanation:

Answer:

8.623

Step-by-step explanation:

ik it

Answer: 8.623

Step-by-step explanation: you move the decimal down 6 points left and then you get your answer

Answer:

(A)Quotient Identity

Step-by-step explanation:

To Prove: [tex]\dfrac{\sin \left(\alpha +\beta \right)}{\cos \left(\alpha +\beta \right)}=\tan \left(\alpha +\beta \right)[/tex]

Rewrite the numerator on the left side of the identity using the sum and difference formulas.

[tex]\dfrac{\sin \left(\alpha +\beta \right)}{\cos \left(\alpha +\beta \right)}=\dfrac{\sin \alpha \cos \beta +\cos \alpha \sin \beta }{\cos \alpha \cos \beta -\sin \alpha \sin \beta }[/tex]

Next, Divide the numerator and denominator by[tex]cos\alpha \text{cos}\beta[/tex]

[tex]=\dfrac{\frac{\sin \alpha \cos \beta +\cos \alpha \sin \beta }{\cos \alpha \cos \beta }}{\frac{\cos \alpha \cos \beta -\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]

Rewrite the fraction from the previous step such that it is a sum or difference of two expressions as shown below

[tex]=\dfrac{\frac{\sin \alpha{\cos \beta }}{\cos \alpha{\cos \beta }}+\frac{{\cos \alpha }\sin \beta }{{\cos \alpha }\cos \beta }}{\frac{{\cos \alpha }{\cos \beta }}{{\cos \alpha }{\cos \beta }}-\frac{\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]

Divide out any common factors in the expression from the previous step.

[tex]=\dfrac{\frac{\sin \alpha }{\cos \alpha }+\frac{\sin \beta }{\cos \beta }}{1-\frac{\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]

The expression from the previous step then simplifies to [tex]\tan \left(\alpha +\beta \right)[/tex] using​ the Quotient Identity

[tex]=\dfrac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }=\tan \left(\alpha +\beta \right)[/tex]

16% of 250 is .16 * 250, which is 40

250% of 16 is 2.5 * 15, which is also 40

So, it's true.

A percentage is a way to describe a part of a whole. The statement that 16% of 250 is equal to 250% of 16 is true.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

The value of 16% of 250 can be written as,

[tex]16\%\ of\ 250\\\\=\dfrac{16}{100} \times 250\\\\=40[/tex]

The value of 250% of 16 can be written as,

[tex]250\%\ of\ 16\\\\=\dfrac{250}{100} \times 16\\\\=40[/tex]

Thus, the statement that 16% of 250 is equal to 250% of 16 is true.

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Answer:

4. x = 2 + 2sqrt(10/3), 2- 2sqrt(10/3)

5. No real solutions

x = 1 + 3sqrt(2) i, 1 - 3sqrt(2) i,

6. x = 1 + sqrt(2), 1 - sqrt(2)

Step-by-step explanation:

4. 3(x - 2)² = 40

(x - 2)² = 40/3

(x - 2) = +/- sqrt(40/3)

x - 2 = +/- 2sqrt(10/3)

x = 2 +/- 2sqrt(10/3)

5. -2(x - 1)² = 36

(x - 1)² = -18

A perfect square can never be negative for real values of x

(x - 1) = +/- i × sqrt(18)

x - 1 = +/- i × 3sqrt(2)

x = 1 +/- i × 3sqrt(2)

6. 4(x - 1)² = 8

(x - 1)² = 2

x - 1 = +/- sqrt(2)

x = 1 +/- sqrt(2)

Answer:

x=2.25

Step-by-step explanation:

Let's break this down:

Saying "y=", is just like saying "0=", so we can say that;

0=4x-9

We need to isolate the variable, and to do that we should add 9 to both sides and cancel it out.

9=4x

Now we need to eliminate the coefficient by dividing both sides by four

[tex]9/4=4x/4[/tex]

Which cancels out four, giving us

2.25=x

Hope this helps and please correct me if I am wrong:)

<3

Using the formula for slope, we calculated that the slope of the line passing through the points (8,10) and (-7,14) is -4/15.

The slope of a line between two points ((x1,y1) and (x2,y2)) can be calculated using the formula for slope: m = (y2 - y1) / (x2 - x1).

In this case, your two points are (8,10) and (-7,14).

Therefore, we can calculate the slope using these points:

m = (14 - 10) / (-7 - 8) = 4/-15 = -4/15.

So, the slope of the line passing through the given points is -4/15.

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Answer:

No, at alpha equals 0.10​, we do not have enough evidence to support the​ county's claim.

Step-by-step explanation:

We are given that a county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 30 miles per hour.

A random sample of 15 vehicles has a mean speed of 31 miles per hour and a standard deviation of 4.7 miles per hour.

Let [tex]\mu[/tex] = true mean speed of the vehicles.

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex]  30 miles per hour   {means that the mean speed of vehicles is lesser than or equal to 30 miles per hour}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 30 miles per hour   {means that the mean speed of vehicles is greater than 30 miles per hour}

The test statistics that will be used here is One-sample t test statistics as we don't know about the population standard deviation;

                        T.S.  = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean speed of 15 vehicles = 31 mph

             s = sample standard deviation = 4.7 mph

             n = sample of vehicles = 15

So, test statistics  =   [tex]\frac{31-30}{\frac{4.7}{\sqrt{15} } }[/tex]  ~ [tex]t_1_4[/tex]

                               =  0.824

Hence, the value of test statistics is 0.824.

Now at 0.10 significance level, the t table gives critical value of 1.345 at 14 degree of freedom for right-tailed test. Since our test statistics is less than the critical value of t as 0.824 < 1.345, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the mean speed of vehicles is lesser than or equal to 30 miles per hour which means that the county's claim is not supported.

Answer:

The dot will be closed, and to the right from -6

Step-by-step explanation:

We can rearrange [tex]m+5>-1 = -6 < m[/tex]

As it is only a < we close the dots. It must go to the left as m is greater than -6 - all numbers greater than a value will be to the right on the number line.

The quadratic function is f(x) = 5(x - 3)² + 2.

A function has an input and an output.

A function can be one-to-one or onto-one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The vertex form of a quadratic function is:

f(x) = a(x - h)² + k

where (h, k) is the vertex of the parabola.

We are given that the vertex is (3, 2), so we have:

h = 3

k = 2

We also know that the parabola passes through the point (4, 7).

We can use this point to find the value of a:

7 = a(4 - 3)² + 2

5 = a

Therefore, the quadratic function is:

f(x) = 5(x - 3)² + 2

This quadratic function has a vertex of (3, 2) and passes through the point (4, 7).

Thus,

The quadratic function is f(x) = 5(x - 3)² + 2.

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Answer:

The answer to your question is the letter B.

Step-by-step explanation:

Data

        √3/2     -2π     4/5    -6.5    7 2/3

Process

1.- Get the decimal values of each data

√3/ 2= 0.87      -2π = -6.28    4/5 = 0.2    -6.5 = -6.5     7 2/3  = 7.67

2.- Order the numbers from greatest to least

            7.67 >  0.87  >  0.2  > -6.28  >  -6.5

or          7 2/3  >  √3/2  >  4/5  >  -2π  >  -6.5

3.- Conclusion

The right answer is B.

Answer:

02a+.03b+.04c=126,

b=a+500,

c=3b

a=300., b=800., c=2400.

Step-by-step explanation:

The amount of each rate of interest given the total simple interest received is

$400, $900 and $2,700 respectively

let

a = 2% investment

= 0.02

b = 3% investment

= 0.03

c = 4% investment

= 0.04

Total interest = (0.02×a) + (0.03×b) + (0.04×c)

143 = 0.02a + 0.03b + 0.04c (1)

b = a + 500 (2)

c = 3b (3)

substitute (3) into (1)

143 = 0.02a + 0.03b + 0.04(3b)

143 = 0.02a + 0.03b + 0.12b

0.02a + 0.15b = 143 (4)

from (2)

b - a = 500 (5)

multiply (5) by 0.02

0.02b - 0.02a = 10

0.02a + 0.15b = 143 (4)

Add

0.02b + 0.15b = 10 + 143

0.17b = 153

b = 900

substitute b into (3)

c = 3b (3)

c = 3(900)

c = 2700

Recall,

b = a + 500 (2)

900 = a + 500

900 - 500 = a

a = 400

Therefore, the amount of each rate of interest given the total simple interest received is $400, $900 and $2,700 respectively

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https://brainly.com/question/15165519

Given:

Given that the radius of the cone is 2 inches.

The height of the cone is 4 inches.

We need to determine the volume of the cone.

Volume of the cone:

The volume of the cone can be determined using the formula,

[tex]V=\frac{1}{3} \pi r^2 h[/tex]

where r is the radius of the cone and h is the height of the cone.

Substituting r = 2 and h = 4 in the above formula, we get;

[tex]V=\frac{1}{3} (3.14) (2)^2 (4)[/tex]

[tex]V=\frac{1}{3} (3.14) (4) (4)[/tex]

[tex]V=\frac{1}{3}(50.24)[/tex]

[tex]V=16.75[/tex]

Thus, the volume of the cone is 16.75 cubic inches.