The sum of two numbers is
60
and the difference is
10
. What are the numbers?

Using proportional reasoning, we can predict that there will be 40 red candies in the large bag.

Using proportional reasoning, we can set up and solve the following equation to determine the number of red candies in the large bag:

P = Proportion of red candies in the large bag

R = Red candies in the small bag

R × (33/9) = P

12 × (33/9) = P

P = 40 red candies in the large bag

Therefore, using proportional reasoning, we can predict that there will be 40 red candies in the large bag.

To learn more about the proportional relationship visit:

brainly.com/question/12917806.

#SPJ1

the orders served by Laura are 22, the orders served by Aldo are 29 and the orders served by Juan are 44.

Total number of orders served on Monday at the school cafeteria = 95

Juan served 2 times as many orders as Laura and Aldo served 7 more orders than Laura.

Let the orders served by Laura be x

Orders served by Juan = 2 x

Orders served by Aldo = x + 7

So, we get the equation as:

x + 2 x + x + 7 = 95

4 x + 7 = 95

4 x = 95 - 7

4 x = 88

x = 88 / 4

x = 22

x + 7 = 22 + 7 = 29

2 x = 2 (22) = 44

Therefore, we get that, the orders served by Laura are 22, the orders served by Aldo are 29 and the orders served by Juan are 44.

Learn more about equation here:

https://brainly.com/question/14323743

#SPJ9

Therefore, the painting should be placed 5/4 feet on each side of the wall.

In the given problem, a 5-foot wide painting should be centered on a 15-foot wide wall. We can determine the length of each side of the painting by subtracting x from each side of the wall.

Therefore, the left side of the equation can be written as:

\(15 - x - 5 - x\)

The physical situation given is that the painting is to be centered on the wall. This means that each side of the wall will have the same amount of space as the painting.

Therefore, the length of each side of the painting can be determined by subtracting x from each side of the wall. The total width of the wall is 15 feet, and the painting is 5 feet wide.

Therefore, the total length of the space on each side of the painting is 5 + x.To find the value of x, we can equate the length of each side of the painting. Therefore, the equation can be written as:

\(15 -x - 5 - x = 5 + x + x\)

Simplifying the equation, we get:

\(10 - 2x = 2x + 5\)

Solving for x, we get:

\(4x = 5x = \frac{5}{4}\)

For such more question on length

https://brainly.com/question/30582409

#SPJ8

First lets find the total number of cookies

12*4=48

48 cookies

Number of cookies eaten

5*2=10

10 were eaten

Cookies left

48-10=38

38/48=19/24

19/24 of the cookies are left

Answer:

38 are left

Step-by-step explanation:

Answer:

Step-by-step explanation:

Vertical cross-section ⇒

Horizontal cross-section ⇒

Vertical cross-section  through base and two lateral faces ⇒

Answer:

In the image

Hope this helps!

Step-by-step explanation:

Answer:

-2<x<8

see below for graph

Step-by-step explanation:

First, we need to solve the inequality.

Inequality: |x-3|<5

Split into two equations:

x-3<5

x-3>-5 (notice how the sign is flipped when we make the number negative)

let's start with x-3<5

add 3 to both sides

x<8

now

x-3>-5

add 3 to both sides

x>-2

The graph is below

the intersection is the solution.

Notice how I made the maroon line go to the right- which shows that it's greater than (for x>-2) and the silver line go to the left, which shows that it's less than (for x<8)

the equation is -2<x<8

Hope this helps!

Answer:

A is the answer because the -T is right at 0

Answer:

\(b.\ cos 70 =\dfrac{4}x\) is the correct answer.

Step-by-step explanation:

First of all, let us label the diagram as shown in the attached figure.

OR = 20'

QS = 16'

\(\triangle OPQ\) is the right angled triangle that we get.

\(\angle P=90^\circ\)

\(\angle O =70^\circ\)

From the given figure symmetry, we can clearly see that:

Side OP = OR - QS

OP = 20 - 16 = 4'

Now, let us use trigonometric identity of cosine in \(\triangle OPQ\).

\(cos\theta = \dfrac{Base}{Hypotenuse}\)

\(cosO= \dfrac{OP}{OQ}\\\Rightarrow cos70^\circ= \dfrac{4}{OQ}\)

Let the distance of ramp, OQ = x'

So, the above ratio becomes:

\(cos70^\circ= \dfrac{4}{x}\)

So, the correct answer is:

\(b.\ cos 70 =\dfrac{4}x\)

Answer:

16

Step-by-step explanation:

The total cost of admission for 6 adults and 6 children to the museum is $71.4.

Total cost refers to the sum of all costs incurred in producing a product, delivering a service, or achieving a particular outcome. It encompasses all the expenses, both direct and indirect, that are associated with a specific activity, project, or process.

According to the given information:

To calculate the total cost of admission for 6 adults and 6 children to the museum, we can substitute the values of "a" and "c" into the given expression "7.1a + 4.8c" and perform the calculations.

Given:

Number of adults (a) = 6

Number of children (c) = 6

Admission cost per adult = $7.10

Admission cost per child = $4.80

Substituting the values into the expression:

7.1a + 4.8c = 7.1 * 6 + 4.8 * 6

Now, we can perform the calculations:

7.1 * 6 = 42.6

4.8 * 6 = 28.8

Adding the results together:

42.6 + 28.8 = 71.4

So, the total cost of admission for 6 adults and 6 children to the museum is $71.4.

To know more about Total cost Visit:https://brainly.com/question/14927680

#SPJ1

Answer:

  $1258.09

Step-by-step explanation:

You want the monthly annuity payment that will let you withdraw $150,000 per year forever from an account earning 8% after 30 years.

In order to withdraw an amount "forever," the withdrawal amount must be equal to the interest earned by the account.

  I = Prt

  150,000 = P(0.08)(1)

  P = 150,000/0.08 = 1,875,000

The value of an ordinary annuity is given by the formula ...

  A = P(12/r)((1 +r/12)^(12t) -1) . . . . . where P is the monthly payment, and r is the annual interest rate earned over a period of t years.

Using the values we know, we can find P:

  1875000 = P(12/0.08)((1 +0.08/12)^(12·30) -1) = 1490.359449P

  P ≈ 1258.09

You would need to deposit $1258.09 each month.

__

Additional comment

The formulas used here assume that the deposits and withdrawals occur at the end of the month.

Answer:

The two lines are neither parallel nor perpendicular to one another.

Step-by-step explanation:

The slope \(m\) gives the orientation of a line.

Make sure that the equation of both lines are in the slope-intercept form \(y = m\, x + b\) (where \(m\!\) is the slope and \(b\) is the \(y\)-intercept) before comparing their slopes.

The equation of the first line \(y = 3\, x - 5\) is already in the slope-intercept form. Compare this equation with the standard \(y = m\, x + b\). The slope of this line would be \(m = 3\).

Rewrite the equation of the second line \(9\, x + 3\, y = 1\) to obtain the slope-intercept equation of that line:

\(3\, y = -9\, x + 1\).

\(\displaystyle y = -3\, x + \frac{1}{3}\).

Thus, the slope of this line would be \(m = (-3)\).

Two lines are parallel to one another if and only if their slopes are equal. In this question, \(3 \ne (-3)\). Thus, the two lines are not parallel to one another.

On the other hand, two lines are perpendicular to one another if and only if the product of their slopes is \((-1)\). In this question, \(3\times (-3) = (-9)\), which is not \((-1)\!\). Thus, these two lines are not perpendicular to one another, either.

Answer:

I believe the answer is B tell me if I'm correct please

The graph of the system of the inequalities is attached.

To graph the inequalities y < -x - 4 and y ≥ (3/5)x + 4, we can start by graphing the corresponding equations and then shade the appropriate regions based on the inequality signs.

Let's begin with the equation y = -x - 4:

Choose a range of x-values to plot.

For simplicity, let's use x-values from -10 to 10.

Substitute different x-values into the equation to find corresponding y-values.

For example:

When x = -10, y = -(-10) - 4 = 10 - 4 = 6.

When x = 0, y = -(0) - 4 = -4.

When x = 10, y = -(10) - 4 = -10 - 4 = -14.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = -x - 4.

Next, let's graph the equation y = (3/5)x + 4:

Again, choose a range of x-values to plot. Let's use the same range of -10 to 10.

Substitute different x-values into the equation to find corresponding y-values. For example:

When x = -10, y = (3/5)(-10) + 4 = -6 + 4 = -2.

When x = 0, y = (3/5)(0) + 4 = 0 + 4 = 4.

When x = 10, y = (3/5)(10) + 4 = 6 + 4 = 10.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = (3/5)x + 4.

Now, let's shade the regions based on the inequalities:

For y < -x - 4, we need to shade the region below the line y = -x - 4.

For y ≥ (3/5)x + 4, we need to shade the region above or on the line y = (3/5)x + 4.

Hence, the region where the shaded regions overlap represents the solution to both inequalities.

Learn more about system of inequalities click;

https://brainly.com/question/29785389

#SPJ1

Answer:

Area of sector of a circle = 28.26 meter²

Step-by-step explanation:

Given:

Side of cube = 12 meter

One white section = sector of a circle

Find:

Area of one white section

Computation:

Radius of circle = Side of cube / 2

Radius of circle = 12 / 2

Radius of circle = 6 meter

One white section = sector of a circle

Area of sector of a circle = [θ/360][π][r]²

Area of sector of a circle = [90/360][22/7][6]²

Area of sector of a circle = [0.25][3.14][36]

Area of sector of a circle = 28.26 meter²

Answer:

The simplest form of √800 is  4√5

Step-by-step explanation:

When finding the simplest form of a square root, we want to express the square root as a product of a whole number and a square root of a prime number. This is because the square root of a prime number cannot be simplified any further, while the square root of a composite number (a number that is not prime) can be further simplified.

In this case, we start by seeing that 800 can be factored as 20*40. To simplify the square root, we need to find the square root of each of these factors. The square root of 20 is not a whole number, but the square root of 40 is √40 i.e. 2√10, which can be further simplified as 2*2√5.

So, √800 = √(2040) = √20 * √40 = 2√10 = 2*2√5 = 4√5

As 4 is a whole number and √5 can't be simplified further, this is the simplest form of the square root of 800.

For more information on simplest form refer:

https://brainly.com/question/564834

https://brainly.com/question/20023959

Although part of your question is missing, you might be referring to this question "What is the simplest form of √ 800 and explain why?"

To calculate the interest charged for the month on a credit card with a balance of $1000 and an APR of 28% after making a $400 payment on the 11th day of a 31-day month, we need to first calculate the average daily balance for the month.

The average daily balance is calculated as follows:

(Previous balance × number of days in billing cycle) + (New charges × number of days since posting of new charges) - (Payments and credits × number of days since payment/credit) / Number of days in billing cycle

In this case, the previous balance is $1000, the number of days in the billing cycle is 31, the new charges are 0, the number of days since posting of new charges is 20 (since the payment posted on the 11th day of the month), the payment/credit is $400, and the number of days since payment/credit is 21. Plugging in these values, we get:

($1000 × 31) + (0 × 20) - ($400 × 21) / 31 = $727.10

Therefore, the average daily balance for the month is $727.10.

To calculate the interest charged for the month, we multiply the average daily balance by the daily periodic rate, which is the APR divided by 365 (since there are 365 days in a year):

$727.10 × (0.28 / 365) × 31 = $19.97

Therefore, the interest charged for the month is $19.97.

Answer:

0.25

Step-by-step explanation:

scale factor=md/od

=0.5/2

0.25

During the exponential phase, e.coli bacteria in a culture increase in number at a rate proportional to the current population. If growth rate is 1.9% per minute and the current population is 172.0 million, the population 7.2 minutes from now can be calculated using the following formula:

P(t) = P ₀e^(rt)where ,P₀ = initial population r = growth rate (as a decimal) andt = time (in minutes)Substituting the given values, P₀ = 172.0 million r = 1.9% per minute = 0.019 per minute (as a decimal)t = 7.2 minutes

The population after 7.2 minutes will be:P(7.2) = 172.0 million * e^(0.019*7.2)≈ 234.0 million (rounded to the nearest tenth)Therefore, the population of e.coli bacteria 7.2 minutes from now will be approximately 234.0 million.

For more such questions on population

https://brainly.com/question/29885712

#SPJ8

The value of x in the similar shapes is 10

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

The similar shapes

On the shapes, we have

x/20 = 5/10

Multiply through the equation by 20

So, we have

x = 20 * 5/10

Evaluate

x = 10

Hence, the value of x is 10

Read more about similar shapes at

https://brainly.com/question/32122930

#SPJ1

Answer:

NOREAL SOLUTION

Step-by-step explanation:

6x2+125=x2

Step 1: Subtract x^2 from both sides.

6x2+125−x2=x2−x2

5x2+125=0

Step 2: Subtract 125 from both sides.

5x2+125−125=0−125

5x2=−125

Step 3: Divide both sides by 5.

Step 4: Take square root.

NOREAL SOLUTION

The equation of the sinusoid function is:

3 Sin πx + 2.

Let's analyze the given options to find the correct equation:

a. 3 Cos πx + 2:

This option is a cosine function with a vertical shift of 2, but it does not have the correct amplitude or period. Therefore, it is not the correct equation.

b. 3 Sin x: This option is a sine function with the correct amplitude, but it does not have the correct vertical shift or period. Therefore, it is not the correct equation.

c. 3 Sin πx + 2: This option is a sine function with the correct amplitude and vertical shift. Let's check if it has the correct period:

To determine if the period is correct, we need to calculate the x-values when the function repeats itself.

In this case, we need to find x-values such that sin(πx) = 0, since the function will reach its maximum and minimum points again at those x-values.

sin(πx) = 0 when πx = 0, π, 2π, 3π, ...

Solving for x, we have:

πx = 0 ⟹ x = 0

πx = π ⟹ x = 1

πx = 2π ⟹ x = 2

πx = 3π ⟹ x = 3

From this, we can see that the function repeats itself every integer value of x, which matches the given information.

Therefore, option (c) is the correct equation: 3 Sin πx + 2.

Option (d) 3 Cos x does not have the correct vertical shift or period, so it is not the correct equation.

Hence, the equation of the sinusoid function is:

3 Sin πx + 2.

Learn more about sinusoid function click;

https://brainly.com/question/21008165

#SPJ1

It is not possible to find a combination using addition and multiplication of the given single-digit numbers that totals exactly 100 while keeping the same order.

To combine the single-digit numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only addition and multiplication so that they total 100 while keeping the same order, we can form the following expression:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9

In this expression, we group the numbers 7 and 8 together to form 78. Then, we add all the other numbers from 1 to 6 and the number 9. Adding them up, we get:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9 = 108

Unfortunately, the sum obtained from this expression is 108, not 100 as required.

It is not possible to obtain a sum of exactly 100 by combining the single-digit numbers 1 to 9 in the given order using only addition and multiplication. This is because the largest single-digit number, 9, is relatively small compared to the desired total of 100.

Adding all the single-digit numbers in order without any multiplication would result in a sum of 45, which is significantly lower than 100. Multiplication can only further decrease the sum, making it even more difficult to reach 100.

For more such question on combination visitr;

https://brainly.com/question/28065038

#SPJ8

The trigonometric measures for the triangle in this problem are given as follows:

The six trigonometric measures for a right triangle are given as follows:

From the given right triangle, the sides are given as follows:

a = 9, b = 4.

Then, applying the Pythagorean Theorem, the length of the sqis given as follows:

h² = 9² + 4²

h² = 97

h = square root of 97.

h = 9.85.

The triangle is given by the image shown at the end of the answer.

More can be learned about the trigonometric measures of a triangle at https://brainly.com/question/24349828

#SPJ1

The range of the graphed function in this problem is given as follows:

[-9, 9].

The values of y in this function are between -9 and 9, inclusive, hence the range of the function is given as follows:

[-9, 9].

Learn more about domain and range at https://brainly.com/question/26098895

#SPJ1

The answers are :

1) AC = 23.25, 2) ML = JL/2 = 6.4, 3) x = 3 and 4) Perimeter = 66.9

Given are circles we need to find the missing measures,

We know that the tangents are perpendicular to the circle, so,

1) Using the Pythagoras theorem,

AC = √10² + 21²

AC = 23.25

2) Similarly,

JL = √16²-9.6²

JL = 12.8

ML = JL/2 = 6.4

3) Tangents on the same circle are equal, so,

43 - 2x = 12x + 1

42 = 14x

x = 3

4) Perimeter = 20.5 + 21.4 + 13 + 12.1

= 66.9

Learn more about tangents of a circle click;

https://brainly.com/question/30951227

#SPJ1

Answer:10cm 5cm 7 Jim's lunch box is in the shape of a half cylinder on a rectangular box. To the nearest whole unit, what is a The total volume it contains? b The total area of the sheet metal in 10 in needed to manufacture it? This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts

Step-by-step explanation:

Note that the notation   "∪C = {x : x ∈ for some S ∈ C} = ∪ { S:S ∈ C}" represents a mathematical statement involving sets.

∪C : This represents the  union (∪) of the sets in C.

{x : x ∈ for some S ∈ C}: This is the description or definition of the elements in the set formed by the union of sets in C.

It states that an element x belongs to the union of   sets in C if and only if x belongs to at least one set S that is an   element of the set C.

= ∪{ S:S ∈ C}   : This means that the union (∪) of sets in C is equal to the union of all sets S that belong to the set C.

In summary,  the statement is saying that the union of sets in C consists of all elements that belong to at least one set in C. It is the combined collection of elements from all sets in C.

Learn more about sets:
https://brainly.com/question/30705181
#SPJ1