Divide 4/5 * 1/10
Blank 1:

7 cars and 4 buses were used on the trip

Let's start by defining some variables to represent the unknowns in the problem:

Let x be the number of cars used.

Let y be the number of buses used.

We know that there were a total of 11 vehicles used, so we can write an equation based on that:

x + y = 11

We also know that the total number of students who went on the trip is 155.

We can use this information to set up another equation:

5x + 30y = 155

This equation represents the fact that the total number of students in cars (5x) plus the total number of students in buses (30y) equals the total number of students (155).

Now we have two equations with two unknowns. We can solve for x and y using a method like substitution or elimination.

Let's use substitution. Solve the first equation for x in terms of y:

x + y = 11

x = 11 - y

Substitute this expression for x into the second equation:

5x + 30y = 155

5(11 - y) + 30y = 155

Simplify and solve for y:

55 - 5y + 30y = 155

25y = 100

y = 4

Now that we know y, we can use the first equation to find x:

x + y = 11

x + 4 = 11

x = 7

Therefore, there were 7 cars and 4 buses used on the trip.

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Answer:

C

Step-by-step explanation:

the degree of a polynomial is the value of the largest exponent of the variable within the expression.

3x³ + 9x² - x - 10

the term 3x³ has the largest exponent in the expression

the polynomial is therefore of degree 3

Answer:

A

Step-by-step explanation:

Since 16.4 is 45% of a number, these two numbers need to be on the same side of the proportions. In A, they are both in the numerator.

The value of x in the angles is 19.

When lines intersect, angle relationships are formed such as vertically opposite angles, adjacent angles etc.

Therefore, let's find the value of x in the intersecting lines.

Hence,

7x - 8 = 6x + 11 (vertically opposite angles)

Vertically opposite angles are congruent and they share the same vertex point.

Hence,

7x - 8 = 6x + 11

subtract 6x from both sides of the equation

7x - 8 = 6x + 11

7x - 6x - 8 = 6x - 6x + 11

x - 8 = 11

add 8 to both sides of the equation

x - 8 + 8 = 11 + 8

x = 19

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Answer:

9/10 > 78/100

Step-by-step explanation:

We can make 9/10 into 90/100, and since they now have the same denominator (Bottom number in fraction), we can now compare the numerators (Top number in fraction). 90 is greater than 78 so we can say that 9/10 > 78/100 (9/10 is greater than 78/100).

The algebraic expression to express "Multiply y by 6, then divide the product by 7" is 6y/7.

We have,

The algebraic expression that represents "multiply y by 6, then divide the product by 7" is:

(6y) / 7

In this expression,

The product of y and 6 is divided by 7.

Thus,

The algebraic expression to express "Multiply y by 6, then divide the product by 7" is 6y/7.

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Step-by-step explanation:

I just did in the other posting. how often did you post it ?

this is a trick question. the triangle at the top is not an isoceles triangle.

we use Pythagoras for an the steps.

so, the left part of the baseline (split by the height) is calculated by

12² = 10² + part²

144 = 100 + part²

part = sqrt(44) = 6.633249581... ft

the other part is then

20 - 6.633249581... = 13.36675042... ft

and the second leg of the large triangle is

leg² = 10² + 13.36675042...² = 278.6700168...

leg = 16.69341238... ft

P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈

≈ 64.69 ft

please see the answer to the other posting for more details.

Answer:

\(\frac{5x-4}{x(x^2+7)^2} = \frac{A}{x} + \frac{Bx+C}{x^2+7} + \frac{Dx+E}{(x^2+7)^2}\)

Step-by-step explanation:

Given the expression \(\frac{5x-4}{x(x^2+7)^2}\), we are to re-write the expression in form of a partial fraction.

Before we write in form of a partial fraction, we need to note the expression at the denominator. Since the expression in parenthesis is a quadratic equation, the equivalent numerator must be a linear expression.

Also the quadratic equation is a repeated form since it is squared. This means that we are to repeat the quadratic equation twice when writing as a partial fraction.

\(\frac{5x-4}{x(x^2+7)^2} = \frac{A}{x} + \frac{Bx+C}{x^2+7} + \frac{Dx+E}{(x^2+7)^2}\)

From the above partial fraction, it can be seen that x² + 7 in parenthesis was repeated twice and their equivalent expressions at the numerator are  both linear i.e Bx+E and Dx+ E where A, B, C, D and E are the unknown constant.

Answer:

the slope is "1"

the y-intercept is "5"

y = x + 5

Step-by-step explanation:

In order to find the slope, we use the slope formula with any pair of points, for example: (1, 6) and (3, 8):

slope = (y2-y1) / (x2 - x1)

in our case:

slope = (8 - 6) / (3 - 1) = 2/2 = 1

then the slope is "1".

Now we write the general "slope-intercept" equation of a line using the slope we found:

y = m x + b

y = 1 x + b

and now use one of the points (for example (3, 8) to find the intercept "b":

(8) = 1 (3) + b

8 - 3 = b

b = 5 (y intercept)

Then the equation of the line can be written as:

y = x + 5

Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

In a 6 sided die, the numbers that are possible to be rolled are

1, 2, 3, 4, 5, and 6.

We know that the numbers 2, 3, and 5 are prime, while 1, 4, and 6 are not.

3 out of the 6 numbers are prime, therefore 3 out of the 6 numbers are not prime.

So the fraction is \(\frac{3}{6}\)

This simplifies to \(\frac{1}{2}\).

Hope this helped!

Answer:

1/2

Step-by-step explanation:

the prime numbers between 1 and 6 inclusive are:  2, 3, 5  (i.e 3 possible outcomes)

the non prime numbers are : 1, 4 and 6 (i.e 3 possible outcomes)

for each roll, the total number of possible outcomes is 6 (because its a 6-sided die)

P(does not roll a prime number) = P (rolls 1, 4 or 6)

= number of possible non-prime outcomes / total number of outcomes

= 3/6

= 1/2

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

The values of x and y are 8 and 10, respectively

The list of the numbers is given as:

4, 7, x, y, 11

The mean and median of the five numbers are the same.

The median is the middle number.

So, we have

Median = x

This means that

Mean = Median = x

The mean is calculated as:

Mean = Sum/Count

This gives

(4+ 7+ x+ y+ 11)/5 = x

Evaluate the sum

(22 + x + y)/5 = x

This gives

22 + x + y = 5x

Evaluate the like terms

4x = 22 + y

Based on the order of the list, we have:

7 < x < y < 11

Assume y = 10

4x = 22 + 10

This gives

x = 32/4

x = 8

Recall that:

7 < x < y < 11

This means that

7 < 8 < 10 < 11

The above is true

Hence, the values of x and y are 8 and 10, respectively

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ANSWER

c

It is c because i did the work and  i know.

The x value of its largest x-intercept is x=2/3

From the question, we have the following parameters that can be used in our computation:

f(x) = 9x^2 - 4

Set the function to 0, to determine teh intercept

9x^2 - 4 = 0

So, we have

9x^2 = 4

Divide both sides by 9

x^2 = 4/9

Take the square root

x = 2/3 and x = -2/3

Hence, teh largest value is 2/3

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∠X = 89°, ∠Y = 90°, ∠Z = 40° ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

→ (2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17°

→ ∠Z=2b+6---- 2*17+6-----> ∠Z=40°

→ ∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°

angle Y and W are supplementary angles

so

→ ∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°

angle X and Z are supplementary angles

so

→ ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

Therefore, the answer is

We can see here that:

6. complementary angles =  ∠JKD and ∠DKH

7. supplementary angles =  ∠HKL and ∠F K L

8. congruent angles =  ∠HKL and ∠F K L

An angle is formed when two rays meet at a common point. The common point is called the vertex of the angle, and the rays are called the sides of the angle. Angles are measured in degrees, with a full circle being equal to 360 degrees.

9. adjacent angles = ∠JKD and ∠DKH

10. vertical angles = ∠HKL and ∠J K F

17. The angle relationships the man made are:

Supplementary angles add up to 180°.

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Answer:

657 pounds

Step-by-step explanation:

Given

Represent the amount of fertilizer with x and the yield with y.

So, we have:

\((x_1,y_1) = (70,630)\)

\((x_2,y_2) = (100,900)\)

Required:

Determine the yield (y) when fertilizer (x) is 73ft^3

Using linear interpolation, we have:

\(y = y_1 + (x - x_1)\frac{(y_2 - y_1)}{(x_2 - x_1)}\)

Substitute the x and y values using

\((x_1,y_1) = (70,630)\) and \((x_2,y_2) = (100,900)\);

We have:

\(y = y_1 + (x - x_1)\frac{(y_2 - y_1)}{(x_2 - x_1)}\)

\(y = 630 + (x - 70)\frac{(900 - 630)}{(100 - 70)}\)

\(y = 630 + (x - 70)\frac{270}{30}\)

\(y = 630 + (x - 70)*9\)

Open bracket

\(y = 630 + 9x - 630\)

\(y = 9x - 630+630\)

\(y = 9x\)

To solve for y when x = 73.

We simply substitute 73 for x

\(y = 9x\)

\(y = 9 * 73\)

\(y = 657\)

Hence, the yield for 73 cubic feet is 657 pounds

Hey there!

\(Answer:\boxed{\text{FALSE}}\)

\(Explanation:\)

\(4(0.2\times-5)=12\)

This equation is false because the value of 4(0.2 * -5) is not equal to 12.

Hope this helps!

Answer:

The answer is "\(n \geq 9\) and \(error < 10^{-4}\)".

Step-by-step explanation:

\(\sum_{n=1}^{\infty} \frac{-1^n}{n 2^n}\\\\\)

Error after \(n^{th}\)term:

\(|R_n|= |\frac{(-1)^{n+1}}{(n+1) 2^{n+1}}| = \frac{1}{(n+1)2^{n+1}}\\\\\to \frac{1}{(n+1)2^{n+1}} < 0.0001\\\\\to 10000< 2^{n+1} (n+1)\\\\\to n\geq 9 \ \ \text{satisfies the inequality}\\\\\to error< 10^{-4}\\\)

Answer:

B, neither

Step-by-step explanation:

21 is not a perfect square or perfect cube.

Answer:

310

Step-by-step explanation:

1.75×39=68.25

241.75+68.25=310

Answer: $310.00

Explanation:

$1.75 × 39 = $68.25

$241.75 + $68.25 = $310.00

The amount of square inches of the log that the furniture maker sanded in terms of π is; 288π in²

The formula for volume of a cylinder is;

V = πr²h

where;

V is volume

h is height

r is radius

Now, we have the parameters as;

r = 2 in

V = 96π in³

Thus;

96π = π(2)²h

h = 96/4

h = 24 in

Formula for surface area of a cylinder is;

S.A =  2πr²h +  2πrh

S.A = 2(π(2)²*24) + 2(π * 2 * 24)

S.A = 192π + 96π

S.A = 288π in²

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The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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Answer:

41

Step-by-step explanation:

\(24*2-7=\\48-7=\\41\)

Answer:

Part 1

(a) There were 2798 patients who only had the protein for Lyme.

Part 2

(b) There were 2516 patients who only had the normal protein.

Part 3

(c) It is not specified in the given information how many patients had none of the proteins. It is only specified that 1538 had the protein for normal patients, CFS, and post-treatment Lyme disease; 1884 had the protein for CFS and Lyme; 408 had the protein for CFS only; 2602 had the protein for CFS; 1731 had the normal protein as well as the one for Lyme; 2798 had the protein for Lyme; 2516 had the normal protein. Based on this information, it is not possible to know how many patients had none of the proteins.

Answer: There are no patients who had none of the proteins.

Step-by-step explanation: Part 1

(a) There were 408 patients who only had the protein for Lyme.

This information can be inferred from the data given: 1884 had the protein for CFS and Lyme, and 2798 had the protein for Lyme. If we subtract 1884 from 2798, we get 914 which is the number of patients who only had the protein for Lyme.

Part 2

(b) There were 2516 patients who only had the normal protein.

This information can be inferred from the data given: 1538 had the protein for normal patients, CFS, and post-treatment Lyme disease, 1884 had the protein for CFS and Lyme, and 2602 had the protein for CFS. If we add 1538, 1884 and 2602, we get 6124, then if we subtract 6124 from the total number of patients (3991) we get 2516 patients who only had the normal protein.

Part 3

(c) There were 0 patients who had none of the proteins.

This information can be inferred from the data given: 1538 had the protein for normal patients, CFS, and post-treatment Lyme disease, 1884 had the protein for CFS and Lyme, 408 had the protein for CFS only, 2602 had the protein for CFS, 1731 had the normal protein as well as the one for Lyme, 2798 had the protein for Lyme, and 2516 had the normal protein. All patients have at least one protein, therefore there are no patients who had none of the proteins.

Answer:

Line AB and the last AB

Step-by-step explanation:

The pressure will be maximum at x = 0.1 cc.

        \(${\displaystyle G=\{(x,f(x))\mid x\in X\}.}\)

Given is that with a dosage of {x} cubic centimeters (cc) of a certain drug, the resulting blood pressure {B} in millimeters of mercury (mm of Hg), is approximated by → B(x) = 50 + 30500x² -183000x³.

The given equation is -

B(x) = 50 + 30500x² -183000x³

For the maximum pressure, we can write -

dB/dx = 0

d/dx (50 + 30500x² - 183000x³) = 0

d/dx (50) + d/dx (30500x²) - d/dx (183000x³) = 0

0 + 61000x - 549000x² = 0

- 549000x² + 61000x = 0

Solving the equation, we get -

x = 0   and   x = 0.1

{x} cannot be 0. So, we can write -

x = 0.1 cc

Therefore, the pressure will be maximum at x = 0.1 cc.

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Answer:

20

You could find 5/⅓

by using 5 × 3

Knowing that:

Any number multiplied by 1, gives the number itself.

Dividing any number by itself gives 1.

Writing 5/⅓ as 5/⅓ × 1 doesn't change the value.

Then I can write 5/⅓ as

5/⅓ × (5×3)/(5×3) = 1

This can become

[5×(5×3)] / [(⅓) × (5×3)]

= 75/(15/3)

= 75/5

= 15

or

12/ 3/5

= [12/ (3/5)] × [(5×3)/(5×3)]

= 12×(5×3) / (3/5)×(5×3)

= (12×5×3) / [(3×5×3)/5]

= 180 / (45/5)

= 180 / 9

= 20