Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Jada and Mackenzie are hosting events that are catered by the same company. Jada plans to have 78 adults and 78 children attend, so the total projected cost of her meals is $3,354. Mackenzie has 58 adults and 76 children on her guest list, so she will pay the caterer $2,800. How much does the caterer charge for each meal?

Every adult's meal costs $____, and every child's meal costs $____.

The next time trains to Aybrin and Bleechtree leave the station together is 280 minutes (or 4 hours and 40 minutes) after 7 am.

To find the next time trains to Aybrin and Bleechtree leave the station together, we need to determine the least common multiple (LCM) of 35 and 40, which represents the time interval at which both train schedules align.

The prime factorization of

35 = 5 x 7,

and 40 = 2 x 2 x 2 x 5

Now, the highest power of each prime factor that appears in either factorization.

So the LCM of 35 and 40 = 2 x 2 x 2 x  5 x  7 = 280.

Therefore, the next time trains to Aybrin and Bleechtree leave the station together is 280 minutes (or 4 hours and 40 minutes) after 7 am.

Learn more about LCM here:

https://brainly.com/question/24510622

#SPJ1

Little's prediction for the second tests median score  is 84

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

The dot plot

The median is the middle number on the dot plot

From the dot plot, the middle number is

Middle = 70

This means that

Median = 70

For the new prediction, we have

New median = 70 * (1 + 20%)

Evaluate

New median = 84

Hence, Little's prediction for the second tests median score  is 84

Read more about dot plot at

https://brainly.com/question/27861010

#SPJ1

(a) The probability that exactly 4 orders will arrive in 30 minutes is 0.1127

(b) The probability that at least 2 orders will arrive in an hour is 0.7586.

(a)  We need to adjust λ to reflect the 30-minute time interval:

λ = 5 orders per hour * 0.5 hours = 2.5 orders in 30 minutes

Now we can plug in the numbers and calculate the probability:

P(X = 4) = ([tex]e^{2.5}[/tex]) *) [tex]2.5^{4}[/tex]/ 4! = 0.1127

(b) We can use the Poisson probability formula again, with λ = 5 orders per hour and x = 0 or 1:

P(X < 2) = P(X = 0) + P(X = 1) = 0.0404 + 0.2010 = 0.2414

Then we can subtract this from 1 to get the probability that at least 2 orders will arrive in an hour:

P(X ≥ 2) = 1 - P(X < 2) = 1 - 0.2414 = 0.7586

Learn more about probability on

https://brainly.com/question/24756209

#SPJ1

The value of x that satisfies the equation -1.5x - 2.7 = 20.1 + 4.5x is -3.8.

To solve this equation, we need to isolate the variable x on one side of the equation. We can do this by using basic algebraic operations, such as adding, subtracting, multiplying or dividing both sides of the equation by the same value.

The first step in solving this equation is to get rid of the constant terms on one side of the equation. We can do this by adding 2.7 to both sides of the equation:

-1.5x - 2.7 + 2.7 = 20.1 + 4.5x + 2.7

Simplifying the left-hand side of the equation, we get:

-1.5x = 20.1 + 4.5x + 2.7

Next, we can move the variable terms to the left side of the equation and the constant terms to the right side of the equation by subtracting 4.5x from both sides:

-1.5x - 4.5x = 20.1 + 2.7

Simplifying the left-hand side, we get:

-6x = 22.8

Finally, we can solve for x by dividing both sides of the equation by -6:

x = -3.8

Therefore, the value of x that satisfies the equation -1.5x - 2.7 = 20.1 + 4.5x is -3.8.

Know more about constant terms   here:

https://brainly.com/question/30198545

#SPJ11

Answer:

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

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, - 1 ) and (x₂, y₂ ) = (3, 8 )

m = [tex]\frac{8-(-1)}{3-(-3)}[/tex] = [tex]\frac{8+1}{3+3}[/tex] = [tex]\frac{9}{6}[/tex] = [tex]\frac{3}{2}[/tex]

Answer:

3/2

Step-by-step explanation:

To find the slope, we use the slope formula

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

    = (8- -1)/( 3 - -3)

    = (8+1)/(3+3)

     = 9/6

    = 3/2

Answer:

5.52 million people with blood group O in KwaZulu-Natal.

Step-by-step explanation:

Multiple alleles refer to the existence of more than two possible alleles (or variations) of a gene within a population. In the case of blood groups, there are multiple alleles for the gene that controls blood type, resulting in the four possible blood groups: A, AB, B, and O.

The blood group AB is the least common in the human population, with only 3% of people having this blood type.

To calculate the number of people who will have blood group O in KwaZulu-Natal, we need to multiply the total population by the percentage of people with blood group O.

9.2 million x (60/100) = 5.52 million people with blood group O in KwaZulu-Natal.

The solution to the system of linear inequalities is the shaded region that satisfies both inequalities.

We have,

To find the solution to the system of linear inequalities:

2x - 3y < 12

y ≤ 2

We first graph the line 2x - 3y = 12:

To graph the line, we can find the x and y intercepts:

When x = 0, we have -3y = 12, then y = -4, so (0, -4) is a point on the line.

When y = 0, we have 2x = 12, then x = 6, so (6, 0) is a point on the line.

Plot these two points and draw the line passing through them:

Next, we shade the region that satisfies the inequality 2x - 3y < 12:

We can choose a test point not on the line, such as (0,0).

Substitute the coordinates into the inequality:

2(0) - 3(0) < 12, which is true.

Now,

We shade the region that satisfies the inequality y ≤ 2:

We shade the region below the horizontal line y = 2:

Therefore,

The solution to the system of linear inequalities is the shaded region that satisfies both inequalities.

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ1

Step 1: Add Equation 2 and Equation 3 to eliminate z.

(-x + y - z) + (x - 3y) = -1 + 3

y - 4y = 2

-3y = 2

y = -2/3

Step 2: Substitute the value of y (-2/3) into Equation 3 to find the value of x.

x - 3(-2/3) = 3

x + 2 = 3

x = 1

Step 3: Substitute the values of x and y into Equation 1 to find the value of z.

3(1) - 8(-2/3) + z = 8

3 + 16/3 + z = 8

9/3 + 16/3 + z = 8

25/3 + z = 8

z = 8 - 25/3

z = 24/3 - 25/3

z = -1/3

Therefore, the solution to the system of equations is:

x = 1

y = -2/3

z = -1/3

Answer:

Step-by-step explanation: 78 +3x+x=180 deg.

                                                 4x=180-78

                                                 4x=102/:4

                                                    x=25.5 deg

Step-by-step explanation:

180 = 78° + 3x°

78° + 3x° = 180°

3x°= 180° - 78°

3x = 102°

x = 102°/3

The height of the skyscraper is D. 156.26 ft

To determine the height of the skyscraper,  we need to consider the following trigonometric identities listed thus;

From the information given, we have that;

Angle, θ = 38 degrees

The shadow casted is the adjacent side of the angle and is 200 ft

The height off the skyscraper is the opposite side

Now, using the tangent identity, we have that;

tan θ = opposite/adjacent

tan 38 = h/200

cross multiply the values, we get;

h = 200(0.7812)

Multiply the values

h = 156. 26 ft

Learn more about trigonometric identities at: https://brainly.com/question/7331447

#SPJ1

Answer:

23/100 equals 23%.

Answer: 23%

Step-by-step explanation: When doing these problems, remember, 100 and a 100% are the same thing, so when you have a problem like this, divide 25 by 100, then multiply by a 100.

Answer:131

Step-by-step explanation:

Use BEDMAS

9x(7+7)+5

=9 x 14 + 5

= 126 + 5

= 131

The required, -x is also 13 units from 0, but to the right of 0 instead of to the left.

The statement about -x is that it is 13 units to the right of 0. This is because the original number, which is 13 units to the left of 0, is represented by a point on the number line to the left of 0. If we negate this number to get -x, then we are reflecting it across the origin (0) to the right side of the number line. This means that the distance of -x from 0 is the same as the distance of the original number from 0, which is 13 units.

Therefore, -x is also 13 units from 0, but to the right of 0 instead of to the left.

Learn more about number line here:

https://brainly.com/question/16191404

#SPJ1

Miles is the number of miles Martin has run, and Total Time is the total time in minutes that he has been running, which is 11Miles + 5.

To create a linear model, we need to find the equation of the line that best fits the data.

We can do this by finding the slope and y-intercept of the line.
First, we need to find the slope, which is the change in y divided by the change in x.

We can choose any two points on the line to calculate the slope.

Let's use the first and second data points:
Slope = (y2 - y1) / (x2 - x1)
Slope = (104 - 60) / (9 - 5)
Slope = 44 / 4
Slope = 11
Now we can use the point-slope form of the equation of a line to find the y-intercept.

We can use the first data point:
The linear model has the form y = mx + b, where y represents the total time (in minutes), x represents the miles run, m is the slope, and b is the y-intercept.

We can use the data points to find the slope (m) as follows: m = (change in total time) / (change in miles)

Using the first two data points, (5, 60) and (9, 104):

m = (104 - 60) / (9 - 5) = 44 / 4 = 11

Now that we have the slope, we can find the y-intercept (b) using one of the data points.

Let's use (5, 60): 60 = 11 * 5 + b 60 = 55 + b b = 5

So the linear model representing Martin's pace is: y = 11x + 5 In this model, x is the miles run, and y is the total time in minutes.
y - y1 = m(x - x1)
y - 60 = 11(x - 5)
y - 60 = 11x - 55
y = 11x + 5
So the linear model that shows the miles Martin has run as the input, and the total time, in minutes, he has been running as the output is
Total Time = 11Miles + 5

For more related questions on Total Time:

https://brainly.com/question/30928238

#SPJ11

The entries of the first row is 3,6. Option B

To add the entries of the first row in the two matrices, we need to first identify the first row of each matrix and then add the corresponding entries together.

Matrix A:

[1  4]

[7  1]

Matrix B:

[2  2]

[4  3]

To add the first rows of these matrices, we simply add the corresponding entries:

1+2      4+2

2          6

Hence, the entries of the first of the two matrices is 2,6

Learn more about matrices at https://brainly.com/question/12661467

#SPJ1

The function equation for the graph above include the following: B. f(x) = -[x] + 3.

In Mathematics and Geometry, a greatest integer function can be defined as a type of function which returns the greatest integer that is less than or equal (≤) to the number.

Mathematically, the greatest integer that is less than or equal (≤) to a number (x) is represented as follows:

y = [x].

By critically observing the given graph, we can logically deduce that the parent function was reflected over the y-axis (negative slope) and it was vertically translated from the origin by 3 units up;

y = [x]

f(x) = -[x] + 3.

Read more on greatest integer function here: brainly.com/question/12165085

#SPJ1

Answer:

6 cm³

Step-by-step explanation:

The figure is a triangular prism with a triangular base with side lengths 3 cm, 4 cm, 5 cm. The height of the prism is 1 cm.

The sides measuring 3 cm and 4 cm form a right angle.

V = BH

where B = area of the base, and

H = height of the prism.

The base is a triangle, so B = (1/2)bh,

where b = base of the triangle, and

h = height of the triangle

V = (1/2)bhH

V = (1/2)(3 cm)(4 cm)(1 cm)

V = 6 cm³

Answer:

side AC

Step-by-step explanation:

is the opposite angle B because it is the furthest you can get on the triangle to be away from point B.

The distance from point B to point A is given as follows:

15,893 ft

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For each angle, we have that:

Hence the position A is obtained as follows:

tan(16º) = 7200/a

a = 7200/tangent of 16 degrees

a = 25109 ft.

The position B is obtained as follows:

tan(38º) = 7200/b

b = 7200/tangent of 38 degrees

b = 9216 ft.

Hence the distance is of:

25109 - 9216 = 15,893 ft.

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

The 6 drawings are grouped to one another

Given data ,

Let the 6 drawings into be divided into two groups of 3 drawings each

And , drawings of each group is similar to one another in some way

where Group 1: ABD

On simplifying the equation , we get

Their curves and the points are in a same order

Group 2: CEF

On simplifying the equation , we get

Their curves and points are oppositely drawn

Hence , the drawings are solved

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

The complete question is attached below :

Group the 6 drawings into two groups of 3 drawings each. The drawings of each group must be similar to one another in some way - they must belong together.

The solution to a system of two linear equations is x = 3; y = 9. the following response is form the solution

1. From the origin, move 3 units right and 9 units up

2. The point of intersection of the two lines

3.Yes, if both lines are the same exact line

4. Can you have exactly two solutions to a Linear system of equations?

5. No, because lines are straight

6. Yes, if the lines are parallel

Parallel lines refers to lines that has equal slopes, such lines do no intersect each other at any point.

Hence we say that no solution is obtained in when linear equations turns out to be parallel lines.

Learn more about system of equation at

https://brainly.com/question/25976025

#SPJ1

Answer:

Step-by-step explanation:

A:  V = πr²h

B:  V = 1/3π(2r)²(2h) = 1/3π(4r²)(2h) = 1/3π8r²h = 8/3πr²h

C:  V = π(2r)²(2h) = π(4r²)(2h) = π8r²h = 8πr²h

D:  V = 1/3πr²(2h) = 2/3πr²h

It should be noted that the ratio between the lengths of the two legs is B. 1: ✓3.

It should be noted that the ratio between the lengths of the two legs will be equal to the tangent.

In this case, tan (30°) = ✓3/3

Tan (60°) = ✓3

Therefore, the ratio between the lengths of the two legs of a 30-60-90 triangle will be 1 : ✓3.

Learn more about ratio on:

brainly.com/question/2328454

#SPJ1

Answer:

Solving the system of equations.

Point form: (3+√25,−3+√2),(3−√25,−3−√2)

Equation form:

x=3+√25,y=−3+√2x=3−√25,y=−3−√2

Step-by-step explanation:

The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.

Let x be the hotel charge before tax in the first city, and y be the hotel charge before tax in the second city. Then we have:
y = x + 1500   (the hotel charge before tax in the second city was $1500 higher than in the first)
0.075x + 0.05y = 825   (the total hotel tax paid for the two cities was $825)
We can use the first equation to solve for y in terms of x:
y = x + 1500
Then we can substitute this expression for y into the second equation:
0.075x + 0.05(x + 1500) = 825
Simplifying this equation, we get:
0.075x + 0.05x + 75 = 825
0.125x = 750
x = 6000
So the hotel charge before tax in the first city was $6000. Using the first equation, we can find the hotel charge before tax in the second city:
y = x + 1500
y = 6000 + 1500
y = 7500
So the hotel charge before tax in the second city was $7500.
Therefore, the answer is: The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.

For more questions on hotel charge

https://brainly.com/question/25569852

#SPJ11

The weight before the party could be any positive number

The weight of the bag of ice after the party was 7/8 pounds. So we can set up an equation:

x - weight used at the party = 7/8

We know that the weight used at the party is the weight before the party minus the weight after the party.

So we can substitute 3x for the weight before the party:

3x - (7/8) = weight used at the party

We don't know the exact weight used at the party, but we do know that it was less than or equal to the weight before the party.

So we can set up another inequality:

weight used at the party ≤ 3x

Putting it all together:

3x - (7/8) ≤ 3x

Simplifying:

-(7/8) ≤ 0

To learn more on Inequality click:

https://brainly.com/question/28823603

#SPJ1

17.55% is the probability for any day, the number of special orders sent out will be exactly 5

The given situation describes a Poisson distribution with a mean of 5 special orders per day. The probability of getting exactly 5 special orders in a day can be calculated using the Poisson probability formula, which is:

P(X = k) = (e^(-λ) * λ^k) / k!

where X is the random variable representing the number of special orders, λ is the mean number of special orders per day, and k is the number of special orders we want to find the probability for.

Plugging in the given values, we get:

P(X = 5) = (e^(-5) * 5^5) / 5!

Simplifying this expression, we get:

P(X = 5) = 0.1755

Therefore, the probability of getting exactly 5 special orders in a day is 0.1755 or 17.55%, rounded to four decimal places.

Intuitively, this means that out of many days, we can expect around 17.55% of them to have exactly 5 special orders sent out. The Poisson distribution is commonly used to model the number of events occurring in a fixed period of time, given a known average rate of occurrence. In this case, the Poisson distribution can be used to estimate the likelihood of a particular number of special orders being sent out in a day.

Know more about Probability here:

https://brainly.com/question/13604758

#SPJ11

Answer: 40 cups per min = 2.5 gallons per hour

Step-by-step explanation: