the sum of two numbers is 56 . the larger number is 16 more than the smaller number. what are the numbers?

(a) Larry took ( 1/3 ) of the sweets in the box.

(b) There were a total of 72 sweets in the box.

(c) The fraction of sweets taken by Keith and Joe are ( 288/9) and ( 144/9 ) respectively.

Keith, Larry, and Joe shared a box of sweets.

Let the total number of sweets be y.

Now, Joe took ( 2/9) of the sweets.

Therefore, the number of sweets Joe took = ( 2/9 )y

Now, Keith took twice as many sweets as Joe.

Therefore, the number of sweets Keith took = 2 × ( 2/9 )y = (4/9) y

Then, the number of sweets Larry too k will be:

= y - ( 2/9 )y - (4/9) y

(a) Then the fraction of sweets Larry took is:

= y - ( 2/9 )y - (4/9) y

= y - [ ( 2 + 4) / 9 ] y

= y - ( 6 / 9 )y

= y - ( 2/3)y

= [ ( 3 - 2 )/3 ]y

= ( 1/3 )y

(b) If Larry took 24 sweets less than the total number of sweets taken by Joe and Keith.

Then,

the number of sweets Keith took + the number of sweets Joe took - 24 = ( 1/3 )y

( 4/9 )y + ( 2/9)y - 24 = ( 1/3 )y

( 6/9 )y - 24 = ( 1/3 )y

( 6/9)y - ( 1/3 )y = 24

[ ( 6 - 3) / 9 ]y = 24

( 3/9 )y = 24

( 1/3)y = 24

y = 24 × 3

y = 72

There were 72 sweets in the box.

(c) The number of sweets Keith took

= (4/9) y

= ( 4/9 ) × 72

= ( 288/9 )

The number of sweets taken by Joe is:

= ( 2/9 )y

= ( 2/9) × 72

= ( 144/9 )

Learn more about fractions here:

https://brainly.com/question/1622425

#SPJ9

The maximum whole number of gigabytes of data she can use while staying within her budget is 3 gigabytes.

From the information, Khloe pays a flat cost of $52 per month and $4 per gigabyte, or part of a gigabyte and she wants her bill to be under $65.

Let the number of gigabytes be represented by x.

Therefore, this will be:

52 + 4x < 65

Collect like terms

4x < 65 - 52

4x < 13

x < 13/4

x < 3.25

Therefore, the highest gigabytes that she can buy will be 3 gigabytes.

Learn more about budget on:

brainly.com/question/663636

#SPJ1

It takes Tom 90 minutes to reach at the work.

Given,

Total time taken by paul = 45 minutes

Time taken by tom = x

According to the question,

the equation will be -

45 = (1/3)x + 15

On solving,

45 - 15 = (1/3)x

30 = (1/3)x

x = 90 minutes

So, it takes, tom 90 minutes to reach

An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

To learn more about linear equations from given link

https://brainly.com/question/12997032

#SPJ4

The line of the graph y= kx +4 goes through the point (2,-2) is given by

y = -3x +4.

As given in the question,

Equation of the line is given by y = kx + 4

Passing through the point (2, -2)

Substitute the value in equation we get,

-2= k(2) + 4

⇒2k = -2 -4

⇒k =-6 /2

⇒k =-3

Equation of the line y= -3x + 4 sketched on graph passing through (2,-2).

Therefore, the line of the graph y = kx +4 goes through the point (2,-2) is given by y = -3x +4.

Learn more about graph here

brainly.com/question/17267403

#SPJ1

Answer:

1199693701

Step-by-step explanation:

URANUS IS 306299

SATURN IS 1200000000

1200000000-306299=1199693701

Answer:

bro this is so easy it's letter d

Step-by-step explanation:

Answer:

D. 8

Step-by-step explanation:

well, let's look at the different parts of the functional expression :

the maximum of 5 is 5, of course.

the maximum of 3 is 3.

the maximum of sin(2x) is the maximum of any sine = 1.

sin(2x) only changes the frequency of the sine wave (the max and min values appear twice as often than for sin(x)), but does not have an impact on the amplitude, which defines the max. and min. values.

sin(2x) is NOT the same as 2×sin(x).

sin(2x) still "waves" between +1 and -1.

so, the total maximum is

5 × 1 + 3 = 8

Answer:

Plug in the numbers to the variables

Step-by-step explanation:

Im not giving ya'll the straight answer because I use it all the time in almost all of my math.

Because you have the value of the variables, all you need to do is plug those variables in and the solve like you usually would (PEMDAS)

Hope this helps and ya'll got this! ;)

We can reduce the rate of refusals in telephone surveys by doing face to face surveys.

A phone study can keep going extremely lengthy, which brings about getting legitimate reactions and knowledge of the respondent's perspective which helps

social event a lot of information. Time limits are a disadvantage of telephone interview studies. Frequently, when you contact individuals at home, they are engaged with different exercises, like having supper or sitting in front of the TV. A few potential interviewees may be hesitant to partake in a meeting because of how much time they dread it will take. Examination can be assembled rapidly in light of the fact that telephone interviews are prompt and gifted questioners can finish a great deal of overviews in a day of work. A great many people have phones, so you have an adequate crowd for get-together a delegate test to finish the study.

Learn more about telephonic surveys, refer:

https://brainly.com/question/19539167

#SPJ4

Answer: x = 49 degrees,      y = 41 degrees

Step-by-step explanation:

Using supplementary angles, we know that x + y + 90 degrees = 180 degrees.

Using complimentary angles, we know that x + 41 degrees = 90 degrees, and x + y = 90 degrees.

Solving first for x,

x + 41 degrees = 90 degrees

x = 90 - 41 degrees

x = 49 degrees

Solving for y,

x + y = 90

Substituting 49 degrees in for x,

y + 49 degrees = 90 degrees

y = 90 - 49 degrees

y = 41 degrees

k = 3

So if your looking at the test I think your looking at, C.

The value of the variable x is 5 and the lengths of PL and LQ are 9 and 48, respectively.

In this problem we find a line segment generated by points P and Q and in which a point L divides the line segment PQ in two sections: PL and LQ. In accordance with the statement, we have the following equations describing the geometric system:

PQ = PL + LQ              

PQ = PL + LQ

57 = (2 · x - 1) + (9 · x + 3)

Now we proceed to clear the variable x with the resulting equation:

57 = 11 · x + 2

55 = 11 · x

x = 5

And finally we find the length of each line segment:

PL = 2 · 5 - 1

PL = 9

LQ = 9 · 5 + 3

LQ = 48

The value of the variable x is 5 and the lengths of PL and LQ are 9 and 48, respectively.

To learn more on line segments: https://brainly.com/question/24069265

#SPJ1

Lamar's office will take 12 weeks to recycle a total of 24 kilograms of paper

Information about the problem:

To solve this problem, we have to state the equation using the information of the problem:

Calculating the recycle rate of Lamar's office, we get:

Rate = Kg recycled / time

Rate = 6 kg/3 weeks

Rate = 2 kg/week

Calculating how many weeks Lamar's office will take to recycle 24 kilograms:

Weeks = Total recycle/ rate

Weeks = 24 kg / 2kg/week

Weeks = 12 weeks

We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

Learn more about algebraic operations at: brainly.com/question/3927786

#SPJ4

Decimal which represents the fraction of the $25.00 Jaime spent is equal to 0.32.

As given in the question,

Total amount in wallet = $25.00

Amount spent = $8.00

Decimal which represents the fraction of the $25.00 Jaime spent

Fraction spent by Jaime = (Amount spent by Jaime)/(Total amount in wallet)

 ⇒Fraction spent by Jaime = ($ 8.00 ) / ($ 25.00)

⇒Fraction spent by Jaime = 8/25

Convert it into decimal

Decimal represents the fraction spent by Jaime = 0.32

Therefore, decimal which represents the fraction of the $25.00 Jaime spent is equal to 0.32.

Learn more about fraction here

brainly.com/question/10354322

#SPJ1

The expression that represents the amount of cookies Bob ate is 1 + 0.5x.

From the information, Bob told Margaret that he ate half if the amount of cookies that Jeff ate. Bob actually ate one more than half of the amount Jeff ate.

Let the amount that Jeff are be represented as x.

Since Bob actually ate one more than half of the amount Jeff ate, this will be:

= (1/2 × x) + 1

= 0.5x +1

Therefore, the expression is 1 + 0.5x.

Learn more about expressions on:

brainly.com/question/22048677

#SPJ1

The values of p and q are -2 and -3 respectively. Hence, (d) is the answer.

Given that:-

The slope of the function on the left is multiplied by p, and q is added to the y-intercept to arrive at the function on the right.

We have to find the values of p and q.

Points of the graph on the left are (-2,0) and (0,1)

Slope of the graph on the left = (1 - 0)/(0 - (-2)) = 1/2

y-intercept of the graph on the left = 1

Hence, the slope intercept form of the graph on the left is :-

y = (1/2)x + 1

Hence, according to the data given in the question, the slope-intercept form of the line on the left is y = (p/2)x + (q + 1)

Also,

Points of the graph on the right are (-2,0) and (0,-2)

Slope of the graph on the right = (-2 - 0)/(0 - (-2)) = -2/2 = -1

y-intercept of the graph on the right = -2

Hence,

Hence, the slope intercept form of the graph on the right is :-

y = -1x -2

Hence,

p/2 =  -1

p = -2

and,

q + 1 = -2

q = -3

To learn more about slope intercept form, here:-

https://brainly.com/question/9682526

#SPJ1

The taller mountain bike frame should be 3.4cm taller.

The equation that can be used to determine the ideal height of the mountain bike frame is:

Mountain bike frame : (2/3 x length of the bike rider's leg) - 10

Mountain bike frame when leg length is 80cm: (2/3 x 80) - 10 =53.3 - 10 = 43.3 cm

Mountain bike frame when leg length is 85cm: (2/3 x 85) - 10 = 56.7 - 10 = 46.7cm

Difference in mountain bike frame :46.7 cm - 43.3 cm = 3.4cm

To learn more about multiplication of fractions, please check: https://brainly.com/question/1114498

#SPJ1

Answer:

a. 105 and 115 employees

b. 185 employees

c. 20 years

Step-by-step explanation:

The total of employees at any given year is y

x is the number of year

then y = 85 + 10x

a. 2nd year: y = 85 + 10(2) = 85 + 20 = 105

   3rd year: y = 85 + 10(3) = 85 + 30 = 115

b. 10th year: y = 85 + 10(10) = 85 + 100 = 185

c: if y = 285

285 = 85 + 10x

10x = 285 - 85

10x = 200

x = 20

Step-by-step explanation:

a.) 105 and 115

b.) 185

c.) 20 yrs

The distance from Tacoma to Seattle is estimated as 25 miles.

Distance is defined as an object's total movement without regard for direction. Distance can be defined as the amount of ground an object had also covered regardless of its beginning or ending point.

Now, as per the given question;

The following are the distances between cities:

120 miles from Portland to Tacoma

145 miles from Portland to Seattle

120+x = 145

x = 145 - 120

x = 25 miles

Therefore, the distance from Tacoma to Seattle is estimated as 25 miles (according to the given graph).

To know more about the distance, here

https://brainly.com/question/26046491

#SPJ4

The complete question is -

Item 17 The cities Portland, Oregon; Tacoma, Washington; and Seattle, Washington, in respective order, lie approximately in a straight line. The distance from Portland to Tacoma is 120 miles. The distance from Portland to Seattle is 145 miles. Find the distance from Tacoma to Seattle.

(see attached figure)

If the triangle is acute, the possible value for the area of the square on the remaining side is 81 inch².

For the triangle to be acute, then the area of both the smaller squares need to be able to be larger than the area of the longer side square when added.

This means that if the triangle is acute, the minimum area of the smaller side is:

= 100 - 36 + 1

= 65 inch²

Of the options, the only area larger than 65 inch² is 81 inch².

Options for this question include:

Find out more on acute triangles at https://brainly.com/question/10753882

#SPJ1

The total drop in temperature, −20∘F, divided by 4 hours equals −5∘F per hour. The temperature dropped 5∘F each hour. (option 1)

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operation.

If the total drop in temperature over 4 hours is −20∘F, in order to determine the temperature drop each hour, divide −20∘F by 4.

Drop each hour = −20∘F / 4 = −5∘F

To learn more about division, please check: brainly.com/question/13281206

#SPJ1

Answer:

last one 0.75x + 0.8(x + 10) = 101

Step-by-step explanation:

Jared made 75% = 0.75
let, his attempts = x

zach made 80% = 0.80
his attempts = (x+10)

total = 0.75x + 0.80(x+10) = 101


Hope it helps!
Brainly?

The participants' most ethical option would have been to let the computer assign the two assignments at random.

A highly transferable skill set that is highly valued in a range of employment routes is analytical and critical reasoning. No matter their field, the most prevalent quality of effective researchers is their ability to think critically and analytically. This skill enables you, whether you're a graduate student or a working person, to efficiently move through the various stages of the research process, including gathering and synthesizing data, assessing conflicting evidence, formulating questions and testing hypotheses, and interpreting and reflecting on your own findings in relation to other studies. In fields that depend on complex decision-making, like healthcare, where errors in judgment can have serious repercussions, it is crucial to develop analytical and critical thinking abilities to lessen biased practices.

To know more about critical reasoning, visit:

https://brainly.com/question/10485927

#SPJ4

Our initial equation:

17h - 7 = 10h - 2 + 7h

I want to get variables ("h") on one side, and numbers on the other, hence I will add 2 to both sides to shift numbers to the left side.

17h - 5 = 10h + 7h

Now I want to simplify the "h" on the right side.

17h - 5 = 17h

Now I will move the variable from the left to the right.

-5 = 0

17h - 17h is zero, think of h being equal to 1 if you don't get it.

-5 = 0 is a false inequality, there are no solutions.

THERE ARE NO SOLUTIONS.

Your question was incomplete. Please refer the content below:

Based on your computations from part I of this exercise, determine which one of the following rules holds for matrices. select all that applies. group of answer choices:

a) A( B + C ) = AB + AC

b) A( B + C ) = BA + CA

c) (A + B)² = A² + 2 AB + B²

d) (AB)² = A²B²

e) (A - B)( A + B ) = A² - B²

The option that is correct is option (a) A( B + C ) = AB + AC.

We know that distributive property holds for all the matrices.

So, we get that:

A( B + C ) = AB + AC

We also know that commutative property does not hold for matrices.

So, we get that:

A( B + C ) = AB + AC ≠ BA + CA

A( B + C ) ≠ BA + CA

(A + B)² = A² + BA + AB + B²

(A + B)² ≠ A² + 2 AB + B² (as AB ≠ BA)

(AB)² = ABAB ≠ A²B²

(A - B)( A + B ) = A² - BA + AB + B² ≠ A² - B²

Therefore, we get that only option (a) A( B + C ) = AB + AC is the correct option.

Learn more about matrices here:

https://brainly.com/question/11989522

#SPJ4

Answer:

70 cars

Step-by-step explanation:

if the ferry took the same number of cars each hour, then you would just do 350/5 = 70

The measure of length TU is 4 units

See attachment for the image of the line

The given parameters are

Line TV = 19 units

Line UV = 15 units

From the question, we understand that the point U is on line TV

This means that

The measure of length TU is calculated as

TU = TV + UV

This gives

TU = 19 - 15

Evaluate the like terms

TU = 4

Hence, the measure of length TU is 4 units

See attachment for the image of the line

Read more about lengths at

https://brainly.com/question/24571594

#SPJ1

Answer: It is linear.

Step-by-step explanation: A linear function must have a degree of 0 or 1. In this case, the slope is 0 but the degree is still 1. 5^1 = 5. So it is linear

Answer:no

Step-by-step explanation: In order for a linear function to be true it has to include a slope intercept