A car is traveling at a constant speed, covering
220 km in 4 hours.
How many hours are needed to cover 550 km?

Since the equations are not given, the equations whose slope will same as that of the slope of the equation 7y - 4x - 14 = 0 i.e. m = 4/7 will be parallel to the line  7y - 4x - 14 = 0.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have the following function -

7y - 4x - 14 = 0

We have the following equation -

7y - 4x - 14 = 0

Rearranging the equation -

7y = 4x + 14

y = (4/7)x + 2

Now, all the lines parallel to the line 7y - 4x - 14 = 0 will have the slope (4/7). Refer to the graph attached.

Therefore, since the equations are not given, the equations whose slope will same as that of the slope of the equation 7y - 4x - 14 = 0 i.e. m = 4/7 will be parallel to the line  7y - 4x - 14 = 0.

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Answer:

Let's solve for x.

9y+8=x

Step 1: Flip the equation.

x=9y+8

Answer:

x=9y+8

Let's solve for x.

−2x+8y=−36

Step 1: Add -8y to both sides.

−2x + 8y + −8y = −36 + −8y

−2x = −8y − 36

Step 2: Divide both sides by -2.

−2x  / −2  =  −8y − 36  / −2

x=4y + 18

Answer:

x=4y + 18

Hope it helps

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Thank you

Answer:

(26, 2)

x = 26

y = 2

Step-by-step explanation:

Given:

9y + 8 = x

-2x + 8y = -36

Substitute (9y + 8) for x in the second equation.

-2(9y + 8) + 8y = -36

Then distribute and solve.

-18y + (-16) + 8y = -36

Combine like terms.

-10y - 16 = -36

-10y = -20

y = 2

Solve for x by substituting the y value (2) into 9y + 8 = x.

9(2) + 8 = x

18 + 8 = x

x = 26

Therefore, the solution is (26, 2) in terms of (x, y).

By answering the presented question, we may conclude that Hence expressions there are 24,360 different methods to give gold, silver, and bronze medals to the top three runners from a group of 30.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator

A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases.

An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

Because the same individual cannot win more than one medal, we must compute the number of ways to give the medals using permutations and combination without repetition. There are 30 options to pick the gold medallist from 30 people, 29 ways to choose the silver medalist from the remaining 29 people, and 28 ways to choose the bronze medalist from the remaining 28 people. As a result, the total number of options is:

30 x 29 x 28 = 24,360

Hence there are 24,360 different methods to give gold, silver, and bronze medals to the top three runners from a group of 30.

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Answer:

I think it would be easier on a pie chart

Explanation

as we can see in the picture, after drawing the angles, we can observe the common angles is

I hope this helps you

Answer: wavelength or frequency

Step-by-step explanation:

The reflectance curve is a plot of the light reflected off a surface as a function of wavelength or frequency. It shows how much light is reflected at each specific wavelength or frequency and can be used to analyze the optical properties of a material.

Answer:

Brand x: 80

Brand y: 45

Step-by-step explanation:

x + y = 125

20x + 15y = 2275

    -20x - 20y = -2500

(+)  20x + 15y = 2275

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

               -5y = -225

y = 45

x + y = 125

x + 45 = 125

x = 80

Answer:

Brand x: 80

Brand y: 45

Null and Alternative HypothesesThe null hypothesis is the statistical hypothesis that assumes that there is no statistical significance between the two variables in the hypothesis. conclude that the proportion of children who suffer from anemia in the town is significantly different from 11%.

In this case, the null hypothesis, H0, is that the proportion of all children in the town who suffer from anemia is 11%.The alternative hypothesis, H1, contradicts the null hypothesis. H1 is that the proportion of all children in the town who suffer from anemia is not 11%\(.H0: p = 0.11H1: p ≠ 0.11\) Test statisticIn order to test the null hypothesis, we need to compute the test statistic. The test statistic in this case is the z-score.

.InterpretationIn layman's terms, we can say that there is strong evidence to suggest that the proportion of children who suffer from anemia in this town is not 11%. The sample data provides enough evidence to reject the claim that 11% of children suffer from anemia in the town. We can therefore

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The margin of error is the degree of inaccuracy that occurs due to random sampling when estimating population parameters. The sample size that produces a margin of error of ±7% is approximately 192.

Sample size calculation is used to determine how many people or elements should be included in a survey or experiment to ensure reliable and valid results.

The sample size and the margin of error are inversely proportional; increasing the sample size will decrease the margin of error, and vice versa.

To calculate the sample size for a given margin of error, you need to use the following formula:

n = (Z² * p * (1 - p)) / E²

Where:

Let's assume a 95% confidence level (Z = 1.96) and a sample proportion of 0.5 (because we don't know the true population proportion).

So, we have:n = (1.96² * 0.5 * (1 - 0.5)) / (0.07²)n = 192.08 ≈ 192.Therefore, a sample size of approximately 192 will be required to produce a margin of error of ±7%.

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a. The limits of integration come from the fact that the triangular region has its base along the x-axis and its height along the line y = -x + 1

A = (-1, 0)

B = (1, 0)

C = (-1, 1)

D = (0, 1)

b. The integral in part (a) is 580/3.

(a) The triangle R can be split into two regions: a triangular region with vertices at (-1,0), (0,1), and (0,0), and a trapezoidal region with vertices at (-1,0), (0,0), and (1,0).

The integral can be expressed as:

∬R(5x+6y)2dA = ∫0^1∫0^(1-x)(5x+6y)2dydx + ∫-1^0∫0^(x+1)(5x+6y)2dydx

The limits of integration come from the fact that the triangular region has its base along the x-axis and its height along the line y = -x + 1, while the trapezoidal region has its longer base along the x-axis and its shorter base along the line y = x + 1.

Therefore, the limits of integration are:

A = (-1, 0)

B = (1, 0)

C = (-1, 1)

D = (0, 1)

(b) To evaluate the integral, we can use the substitution u = 5x + 6y, v = 6x - 5y. This transforms the integrand to u^2, and the limits of integration become:

0 ≤ u ≤ 5

-1/3(u-5) ≤ v ≤ 1/3(u+5)

Using this substitution, we have:

∬R(5x+6y)2dA = ∫0^5∫-1/3(u-5)^(1/3)(u+5)^(1/3)u^2dvdu

Evaluating this integral gives:

∬R(5x+6y)2dA = 580/3

Therefore, the integral is 580/3.

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Answer:

541.67m²

Step-by-step explanation:

Step 1

We find the third angle

Sum of angles in a triangle = 180°

Third angle = Angle V = 180° - (63 + 50)°

= 180° - 113°

Angle V = 67°

Step 2

Find the sides x and v

We find these sides using the sine rule

Sine rule or Rule of Sines =

a/ sin A = b/ Sin B

Hence for triangle VWX

v/ sin V = w/ sin W = x / sin X

We have the following values

Angle X = 50°

Angle W = 63°

Angle V = 67°

We are given side w = 37m

Finding side v

v/ sin V = w/ sin W

v/ sin 67 = 37/sin 63

Cross Multiply

sin 67 × 37 = v × sin 63

v = sin 67 × 37/sin 63

v = 38.22495m

Finding side x

x / sin X= w/ sin W

x/ sin 50 = 37/sin 63

Cross Multiply

sin 50 × 37 = v × sin 63

x = sin 50 × 37/sin 63

x = 31.81082m

To find the area of triangle VWX

We use heron formula

= √s(s - v) (s - w) (s - x)

Where S = v + w + x/ 2

s = (38.22 + 37 + 31.81)/2

s = 53.515

Area of the triangle = √53.515× (53.515 - 38.22) × (53.515 - 37 ) × (53.515 - 31.81)

Area of the triangle = √293402.209

Area of the triangle = 541.66614164081m²

Approximately to the nearest tenth = 541.67m²

Answer: 10

Step-by-step explanation:

4 + 2 + 4 = 10

Josiah has to choose from 32 different outfit.

"According to Fundamental Counting Principle, the total number of outcomes of two or more independent events is the product of the number of outcomes of each event."

For given situation,

Let event A: choosing pair of pants

⇒ n(A) = 4

event B: choosing t-shirt

⇒ n(B) = 2

event C: choosing shoes

⇒ n(C) = 4

Using the Fundamental Counting Principle the number of outfits would be,

= 4 × 2 × 4

= 32

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The population size of the protozoa after seven days, starting with an initial population of five members and a constant relative growth rate of 0.469 per member per day, can be calculated using the formula\(P(t) = 5 * e^{(0.469 * 7)\).

Part 1 of the question establishes that the relative growth rate of the protozoa population is 0.469 per member per day. This information helps us define the differential equation that represents the growth: dP/dt = 0.469P.

Part 2 introduces the exponential growth formula for population growth, which states that \(P(t) = P(0)e^{kt\) where P(t) is the population size at time t, P(0) is the initial population size, k is the growth rate, and e is the base of the natural logarithm.

To find the population size after seven days, we substitute the given values into the formula: \(P(t) = 5 * e^{(0.469 * 7)\). Evaluating this expression yields the final answer, which represents the population size of the protozoa after seven days.

Note: The calculation itself is not included in the answer as the model response is limited to explaining the approach.

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Answer:

hope this helps

Step-by-step explanation:

The expression for V(t), the value of Rick's snowmobile, in dollars, after t years can be given by:

V(t) = $10,500 * (1 - 0.14)^t

Simplifying this expression, we get:

V(t) = $10,500 * 0.86^t

So, the required expression for V(t) is:V(t) = 10,500 * 0.86^t

Answer:

For the first question, the answer is 32 oz.

For the second question, the answer is 16 oz.

Step-by-step explanation:

For the first one, since there are 16 ounces in a pound, we can assume that since she has 3 pounds of fudge, she would have 48 ounces. She then eats one pound of fudge, which means we subtract 16 from 48 getting us to 32 ounces.

For the second question, it states that she gives one half of her fudge to her sister. 2 times 1/2 is 1, and since there are 16 ounces in a pound, she therefore gave 16 ounces of fudge to her sister.

Answer:

1. 32 ounces

2. 16 ounces

Step-by-step explanation:

First, you have to subtract. The equation for the subtraction is 3-1 because the student took 1 pound of fudge away from the 3 pounds she already has. And 3-1 equals 2. Now, you have to convert 2 pounds to ounces. Lastly, multiply 2 by 16 as it says in the picture (it says 16 ounces equals 1 pound). The answer to this equation can be expressed as 32 or 32 ounces.

First, you have to take information from the previous question which is that she has 2 pounds of fudge left. Then, she gives \(\frac{1}{2}\) of the fudge to her sister, so you have to divide 2 by \(\frac{1}{2}\) which is 1. Now, you have to express 1 as ounces as shown in the picture. You just have to multiply 1 by 16 which is 16. Therefore the answer can be expressed as 16 or 16 ounces.

Answer:

a. A + C < B + C

Step-by-step explanation:

when we know that A < B, then adding the same amount to both sides did not change the relationship between both sides.

this is like having a balance with 2 cups. one side is heavier than the other, so the heavier cup is down.

if we add the same weight to both cups, the situation will not change.

that is why a. is the right answer.

b. would only be right, if C is negative.

for positive C the same argument as for A applies. a smaller amount (or weight) stays smaller also after multiplying both sides by the same number.

but because this option would only be right for a subset of the possible values, this is not true in general.

c.

this is not true at all.

if we multiply the expression by -1, then the inequality sign has to flip. < becomes >, > becomes <.

which did not happen here.

Answer: -35/18

Step-by-step explanation: Hello!

The main thing that you need to know when dividing fractions is what the reciprocal is. Here is an example of finding the reciprocal:

1/2 divided by 2/3 = 1/2 x 3/2.

Basically, you flip the second fraction upside down (Put the number under the fraction line over the fraction line and put the number above the fraction line under the fraction line).  Then, you multiply the two fractions.  Then, you will find the answer.  Here is how to do that with the problem you have:

5/3 divided by (-6/7) = ?

After finding the reciprocal, you would get:

5/3 x (-7/6)

To find the answer, multiply the numerators together (5 and -7) and the denominators (3 and 6) together.

For the new numerator, you get -35.  For the new denominator, you get 18.  Put the new numerator above the fraction line and the new denominator below the fraction line.

The answer is:

-35/18

The distance between the bird (B) and plane (P) exists at 10,779 feet.

Given the figure attached,

PT = OB = 7000 ft

PB = OT = x feet

and angle of elevation (∠POT) = 30°

By applying the Tan rule in the triangle POT,

tan 33° = Opposite side/Adjacent side = PT/OT

tan 33° = 7000/x

x = 7000/tan33°

x = 10779 feet

The distance between the bird (B) and plane (P) exists at 10,779 feet.

Therefore, the correct answer is option D. 10779 feet.

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The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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The solution to the given system of linear equations is x = -2 and y = -8. That is, (-2, -8).

From the question, we are to determine the solution to the given system of linear equations.

The given system of linear equations is

y = 5x + 2         ---------- (1)

4x - y = 0          ---------- (2)

Substitute equation (1) into equation (2)

4x - y = 0

4x - (5x + 2) = 0

4x - 5x -2 = 0

-x -2 = 0

-2 = x

x = -2

Substitute the value of x into equation (1)

y = 5x+ 2

y = 5(-2) + 2

y = -10 + 2

y = -8

Hence, the solution is x = -2 and y = -8

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Answer:

6 for $1.26 is better

Step-by-step explanation:

$1.26/6 = $0.21 per can

$1.98/9 = $0.22 per can

Answer:

y=16

Step-by-step explanation:

Notice that the first equation was multiplied by 4, so you have to multiply the result by 4 to keep it as a true equation

The variance of the sample means will be 0.3428.

What is Variance of sample means?

The variance of the sampling distribution of the mean is the population variance divided by the sample size.

Given that;

A uniform continuous distribution has a maximum of 14 and a minimum

of 2.

Samples of size 36 are drawn from the distribution.

Now,

The population variance = 14 - 2

                                      = 12

And, Sample size = 36

Since, The variance of the sample means is defined as;

= Population variance / Sample size

Substitute all the values, we get;

= 12 / 35

= 0.3428

Thus, The variance of the sample means will be 0.3428.

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The value of the triple integral will be zero so the flux of the given surface is zero.

To compute the flux using the Divergence Theorem, we need to follow these steps:

1. Find the divergence of the vector field F(x, y, z) = (zx, yx³, x²z).
2. Set up the triple integral over the solid region bounded by y = 4 - x²z² and y = 0.
3. Evaluate the triple integral to find the flux.

Step 1: Find the divergence of F.
∇ · F = (∂/∂x, ∂/∂y, ∂/∂z) · (zx, yx³, x²z) = (∂/∂x)(zx) + (∂/∂y)(yx³) + (∂/∂z)(x²z) = z + 3yx² + x²

Step 2: Set up the triple integral.
The solid region is bounded by y = 0 and y = 4 - x²z². To set up the integral, we need to express the limits of integration in terms of x, y, and z.

Let's use the following order of integration: dy dz dx.
For y, the bounds are 0 to 4 - x²z².
For z, the bounds are -2 to 2 (since -2 ≤ z ≤ 2 when y = 4 - x²z², x ∈ [-1, 1]).
For x, the bounds are -1 to 1 (due to the x² term in the bounding equation).

Step 3: Evaluate the triple integral.
Flux = ∫∫∫ (z + 3yx² + x²) dy dz dx, with the limits as described above.

The value of the triple integral will be zero so the flux of the given surface is zero.

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The answer is B

It's not A, C, or D, because they all are stated as integers, which cannot be irrational

The values of x and y are given by 8 and 9 respectively.

Since the quadrilateral is a parallelogram. So the opposite sides should be equal and parallel.

So,

4x-17 = 2x-1

4x-2x = 17-1

2x = 16

x = 8

Again the angles (3y+5) and (5y-13) are alternating angles with respect to parallel opposite sides of parallelogram and diagonal as transversal. So they are equal.

3y+5 = 5y-13

5y-3y = 13+5

2y = 18

y = 18/2

y = 9

So the values are, x=8 and y=9.

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According to the information, we can infer that the number of ounces of water, x, that Will could have put in each cup is 8 ounces.

Will initially had a cooler filled with 144 ounces of water. After using 16 ounces to fill his water bottle, there were 144 - 16 = 128 ounces of water remaining in the cooler.

Will then took out 16 plastic cups for his teammates. Since the same amount of water was put in each cup, the remaining amount of water, 128 ounces, needs to be divided equally among the cups.

Dividing 128 ounces by 16 cups gives us 8 ounces of water for each cup.

So, Will could have put 8 ounces of water in each cup.

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Answer:

60001 miles

Step-by-step explanation:

Given

\(Total\ Distance = 180000\)

Let the cars be: \(Car\ A, Car\ B\ and\ Car\ C\)

Assume that Car A has the minimum mileage of x.

\(Car\ A = x\)

The other cars would be:

\(Car\ B = x + 1\)

\(Car\ C = x + 2\)

This implies that Car C has the highest mileage

Required

Determine the possible minimum number of miles

Since the total distance is 180000, then:

\(Car\ A + Car\ B + Car\ C = 180000\)

Substitute values for Car A, B and C

\(x + x + 1 + x + 2 = 180000\)

Collect Like Terms

\(x + x + x = 180000-1-2\)

\(3x = 179997\)

Divide both sides by 3

\(\frac{3x}{3} = \frac{179997}{3}\)

\(x = \frac{179997}{3}\)

\(x = 59999\)

The car with the most mileage is Car C

So:

\(Car\ C = x + 2\)

Substitute 59999 for x in \(Car\ C = x + 2\)

\(Car\ C = 59999 + 2\)

\(Car\ C = 60001\)

The minimum distance travelled by Car C is 60001 miles