Gary has 20 more candies than Mary. If Gary gives Mary 19 of his candies, Mary would have how many more candies than Gary?
Help!

Tammy received 19 phone calls on the first evening, 13 phone calls on the second evening, and 76 phone calls on the third evening.

Let's use algebra to solve the problem.

Let x be the number of phone calls Tammy received on the first evening.

According to the problem, she received 6 fewer calls on the second evening than on the first evening. This means that the number of phone calls she received on the second evening is x - 6.

The problem also states that she received 4 times as many calls on the third evening as she did on the first evening. This means that the number of phone calls she received on the third evening is 4x.

We know that Tammy received a total of 108 phone calls over the three evenings. We can use this information to set up an equation:

x + (x - 6) + 4x = 108

Simplifying the equation:

6x - 6 = 108

Adding 6 to both sides:

6x = 114

Dividing both sides by 6:

x = 19

Therefore, Tammy received 19 phone calls on the first evening, 13 phone calls (19 - 6) on the second evening, and 76 phone calls (4 x 19) on the third evening.

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Complete question is:

Over the last three evenings, Tammy received a total of 108 phone calls at the call center. The second evening, she received 6 fewer calls than the first evening. The third evening, she received 4 times as many calls as the first evening. How many phone calls did she receive each evening?

Answer: 5/2x-3

Step-by-step explanation: you would subtract 6 from both sides.

5x = 2y + 6

-6            -6

6-6=0 so they would cross out. and you can't subtract 5x from 6 because they aren't like terms. Your new equation would look like 5x-6 = 2y.

Now you need to get the y alone. To do that you need to divide everything by 2 so that the 2y crosses out. 5x-6 = 2y

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

                                                                             2    2    2

I'm trying to visually show it sorry if it looks weird. one you divide everything. (5/2) (-6/2) (2/2) you'll need to clean everything up.

Since you can't simply 5/2 leave it as a fraction. Which makes your answer: 5/2x - 3 = y or y = 5/2x - 3

Answer:

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

Recall triangle angle sum property, the sum of three interior angles is 180°.

Add up the three angle measures, then solve the equation for x:

Substitute the value of x and find the value of each angle:

Answer:

The system of equation is y=12x+5

Step-by-step explanation:

If a set of grades have a large range and a small standard deviation, it means that there are few students with high marks and few with low marks. Most students falls in the average region.

Range is the difference between the maximum value and the minimum value. So for the range to be higher, there must be at least one very high grade and at least a very low grade. If the maximum mark scored by the highest scorer is 95 and 10 for the lowest, the range will be 95- 10 = 85.

If one scored 99 and the lowest scorer got 5, then the range is 99-5 = 94. So higher the range means there is great difference between the highest and lowest grade.

Standard deviation means how much the value deviates from average. If it is low, that means most of the students scored near to the average.

So high range and low standard deviation means, there are few high scorers and few low scores. But most students falls in the average category.

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The required, Rich's monthly mortgage payment will be $1,246.91.

A mortgage payment is the amount of money that a borrower pays to a lender in order to repay a home loan.

Here,
The amount that Rich is financing with the mortgage is the difference between the total cost of the home and the down payment:

Amount financed = $244,800 - 0.15($244,800) = $208,080

To calculate the monthly mortgage payment, we can use the formula for the present value of an annuity,
[tex]PMT = (PV * r) / (1 - (1 + r)^{-n}[/tex]

First, we need to calculate the monthly interest rate. Since the annual interest rate is 5.25%, the monthly interest rate is:

r = 0.0525 / 12 = 0.004375

Next, we need to calculate the total number of payments. Since Rich is taking out a 25-year loan, he will be making 25 x 12 = 300 monthly payments.

Now we can plug these values into the formula and solve for PMT:

PMT = ($208,080 × 0.004375) / (1 - (1 + 0.004375)^(-300))

= $1,246.91

Therefore, Rich's monthly mortgage payment will be $1,246.91.

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The area of sector RFS is approximately 8π square inches, and the measure of the central angle in radians is approximately 2π/3 radians.

What is the central angle?

A central angle is an angle with endpoints and located on a circle's circumference and a vertex located at the circle's center. A central angle in a circle determines an arc.

To determine the measure of the central angle in radians, we can use the formula:

radians = degrees * (π / 180)

So, for the central angle of 120°:

radians = 120 * (π / 180) = 2 * π / 3

The measure of the central angle in radians is approximately 2 * π / 3 radians.

To find the arc length of RS, we can use the formula:

arc length = (central angle / 360) * circumference

The circumference of the circle is given by 2 * π * r, where r is the radius:

circumference = 2 * π * 4 = 8 * π

So the arc length is:

arc length = (120 / 360) * (8 * π) = 4 * π / 3

The arc length of RS is approximately 4 * π / 3 inches.

To find the area of sector RFS, we can use the formula:

area = (central angle / 360) * π * r²

So the area of sector RFS is:

area = (120 / 360) * π * (4)² = 8 * π

Therefore, The area of sector RFS is approximately 8π square inches, and the measure of the central angle in radians is approximately 2π/3 radians.

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Answer:

Arch length = 8pi/3

Area of sector = 16pi/3

Central angle in radians = 2pi/3

Step-by-step explanation: see picture-

Answer:

x=12

Step-by-step explanation:

12 =2 (x - 6)

Solve for x.

Divide each side by 2

12/2 =2/2 (x - 6)

6 = x-6

Add 6 to each side

6+6 = x-6+6

12 = x

Answer:

x = 12

Step-by-step explanation:

Simplify  both sides of the equation

Turn the equation around

Add 12 to both sides

Divide both the sides by 2

Answer:

9 science books

Step-by-step explanation:

Step 1) 36 - 17 = 19

Step 2) 19 - 10 = 9

The probability that the last red ball was the 8th ball out is 3/10

Number of red  balls = 3 red balls

Number of black balls = 7 black balls

Then you randomly draw the balls out one by one without replacement.

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The equation will be

Probability = Number of favorable outcomes / Total number of outcomes

Total number of outcomes = 3 + 7

= 10

Substitute the values in the equation

The probability that the last red ball was the 8th ball out = 3/10

Therefore, the probability is 3/10

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The number of solutions of the system of equations is given as follows:

D. Infinitely many solutions.

The system of equations is defined as follows:

The second equation was obtained multiplying the first equation by 3, meaning that the two equations are multiples, and thus the system of equations has an infinity number of solutions and the correct option is given by option D.

The system of equations is defined as follows:

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Answer: H. -2 or 8/3

Step-by-step explanation:

3x^2-2x-16=0

Multiply 3 times 16

x^2-2x-48=0

find two numbers that will add up to equal -2 and will be multiplied to get -48. (-8 and 6)

(x-8)(x+6)

divide both numbers by 3 but since you cannot divide 8 and 3 you will move the 3 in front of the x.

(3x-8)(x+2)

Set both equal to 0.

3x-8=0    x+2=0

x= 8/3      x=-2

Answer:

maximum score = 92

Step-by-step explanation:

the maximum score is the largest value in the data set.

maximum score = 92

The value of x to the nearest tenth are as follows;

x = 47.0 units.

x = 25.1 units.

x = 23.8 units.

x = 29.7 units.

x = 21.1°.

x = 39.6°.

x = 58.0°.

x = 72.9°.

From the image attached above, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:

Opposite side = x.

Adjacent side = 25.

Therefore, we would determine the value of x by using Tan trigonometric function:

Tanθ = Opposite side/Adjacent side

Tan45 = 25/x

x = 25Tan62

x = 47.0 units.

For right-angled triangle 3, we have:

Sin26 = 11/x

x = 11/0.4384

x = 25.1 units.

For right-angled triangle 4, we have:

Sin48 = x/32

x = 32sin48

x = 23.8 units.

For right-angled triangle 5, we have:

Cos12 = 29/x

x = 29/0.9782

x = 29.7 units.

For right-angled triangle 6, we have:

Cosθ = 14/15

θ = cos⁻¹(0.9333)

θ = 21.1°.

For right-angled triangle 7, we have:

Tanθ = 19/23

θ = tan⁻¹(0.8261)

θ = 39.6°.

For right-angled triangle 8, we have:

Cosθ = 9/17

θ = cos⁻¹(0.5294)

θ = 58.0°.

For right-angled triangle 9, we have:

Sinθ = 43/45

θ = sin⁻¹(0.9556)

θ = 72.9°.

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The slope and y-intercept of the equation y= -4/3 x-2 are -4/3 and -2 respectively.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

In the given graph two lines are plotted.

Part A: From the graph, the two equations are intersected at (-1.5, 0) and the solution is (-1.5, 0).

Part B: Slope and y-intercept

Equations of lines from the graph are y=3/4 x+1 and y= -4/3 x-2.

For the equation y=3/4 x+1,

Compare, y=3/4 x+1 with y=mx+c, we get

Slope (m)= 3/4 and the y-intercept (c)=1

For the equation y= -4/3 x-2,

Compare, y= -4/3 x-2 with y=mx+c, we get

Slope (m)= -4/3 and the y-intercept (c)=-2

Therefore, the slope and y-intercept of the equation y= -4/3 x-2 are -4/3 and -2 respectively.

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Answer:

the smallest number is 1079

Step-by-step explanation:

Let the numbers be x and y

a) The values are given as follows:

i) x1: -0.5.

ii) x2: -0.280125.

b) The solution of the equation is of: -0.25410169644.

The equation in this problem is given as follows:

y = (x³ - 1)/4.

The solution is obtained using a iterative solution method, until the difference between previous iterations is less than 10^-6, as the solution is exact to 6 decimal places.

Then the values are given as follows:

x1  = -1 -> attributed.

x2 = ((-1)³ - 1)/4 = -0.5.

x3 = ((-0.5)³ - 1)/4 = -0.28125.

x4 = ((-0.281255)³ - 1)/4 = -0.25556212524.

x5 = ((-0.25556212524)³ - 1)/4 = -0.25417281837

x6 = ((-0.25417281837)³ - 1)/4 = -0.25410513385

x7 = ((-0.25410513385)³ - 1)/4 = -0.25410185521.

x8 = ((-0.25410185521)³ - 1)/4 = -0.25410169644. -> difference less than six decimal places.

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An approximate solution to an equation is found using this iterative process.

Xₙ₊₁= (Xₙ)³ - 1 / 4 and x₁= -1

a)

(i) Work out the value of x₂

(ii) Work out the value of x₃

b) Work out the solution to 6 decimal places

Step-by-step explanation:

Sure, I'd be happy to help!

5 feet 7 inches is equivalent to 170.18 cm.

Answer: acute

Step-by-step explanation:

   This triangle does not have any right angles (90°), or any angles larger than a right angle, so it is an acute triangle.

V Prism is V = B × h=9.5*4=38

the volume of a sphere is V = 4/3 π r³=4/3*22/7*9.5=10.47

V=10.47+38=48.476

A measurement of three-dimensional space is volume. It is frequently expressed in numerical form using SI-derived units, as well as different imperial or US-customary units. In contrast to how much space the container actually occupies, the volume of a container is typically thought of as its capacity, or the amount of fluid it could hold. Volume was initially measured using naturally occurring vessels of a comparable shape and then with standardized containers. Arithmetic formulas can be used to quickly calculate the volume of several straightforward three-dimensional shapes. If a formula for the shape's boundary is known, it is possible to use integral calculus to determine the volumes of more complex shapes. objects in the zero, one, and two dimensions have no volume.

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Number of Defects = 12,500 * 0.01 = 125Therefore, we can predict that if 12,500 flashlights are made, then 125 of them will be defective.

The formula for this problem is: Number of Defects = (total number of items)*(percent of defects)For this problem, we know that the total number of items is 12,500 and the percent of defects can be found by taking the 5 defective items out of the 500 items produced, which is 1%.Plugging these numbers into the formula, we get :Number of Defects = 12,500 * 0.01 = 125Therefore, we can predict that if 12,500 flashlights are made, then 125 of them will be defective.

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There are a total of binom n2 binom n-21 + binom n3 possible committees with at least 2 secretaries.

Assume that there are n total secretaries employed by the business.

Either we can select 2 secretaries and 1 non-secretary member, or we can select all 3 members to be secretaries in order to form a committee with at least 2 secretaries.

Out of n, there are binom n2 ways to select two secretaries, and binom n-21 ways to select a non-secretary member from the remaining n-2 non-secretaries.

This means that there are binom n ways to form a committee with 2 secretaries and 1 non-secretary member.

There are binom ways to select each of the three members to serve as a secretary.

There are a total of binom n2 binom n-21 + binom n3 possible committees with at least 2 secretaries.

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Answer:

Both data sets represent multiplicative relationships. In Table A, y is 2.5 times x, and in Table B, y is 3 times X

Step-by-step explanation:

Self-explanatory

Every value of y in Table A is 2.5 times  x value

and

every value of y in table B is 3 times x value

Answer:

-1/2-4x/5=1/2-2x

Starting from the left side, we can simplify:

-1/2 - 4x/5 = 1/2 - 2x

Next, we can isolate x by adding 2x to both sides:

-1/2 - 4x/5 + 2x = 1/2 - 2x + 2x

-1/2 + 2x/5 = 1/2

Adding 1/2 to both sides:

0 + 2x/5 = 1

Finally, solving for x:

2x/5 = 1

Multiplying both sides by 5:

2x = 5

Dividing both sides by 2:

x = 5/2

7x² + 9x² = -6x² - 7x

Combining like terms:

16x² = -6x² - 7x

Adding 6x² to both sides:

22x² = -7x

Dividing both sides by -7:

-22x²/-7 = 7x/-7

-22x²/7 = -7x/7

-22x²/7 = -x

Multiplying both sides by -7:

22x² = x

Dividing both sides by 22:

x² = x/22

Since this equation states that x² equals x divided by 22, it has no real solutions for x.

-7x² + 6 = x² - 7x²

Combining like terms:

-8x² + 6 = 0

Adding 8x² to both sides:

-8x² + 8x² + 6 = 0 + 8x²

6 = 8x²

Dividing both sides by 8:

6/8 = 8x²/8

3/4 = x²

Taking the square root of both sides:

sqrt(3/4) = sqrt(x²)

x = +/- sqrt(3/4)

Answer:

i think this the answer

Step-by-step explanation:

26×14=ans

20×14+6×14=the same answer

10×26+4×26=same answer

The measure of center should the charity use to accurately represent the data is The mean of 49 is the most accurate to use to show that they have plenty of money, the correct option is C,

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Median represents the middle value of the given data when arranged in a particular order.

We are given that;

The list of donation is as follows

11, 18, 35, 39, 45, 45, 46, 47, 49, 49, 50, 50, 50, 50, 56, 57, 58, 59

Now,

Mean is the middle term of the data

Here,

Middle term of data=49

Therefore, the mean of the given list will be 49.

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Answer: The answer is 3 slices

Step-by-step explanation:

if you cut a pizza into 12 peices and devide it by 4 people each person gets 3

The area of the shaded region found using trigonometric ratios is about 86.6 square centimeters

Trigonometric ratios are expressions of the relationship between the interior angle of a right triangle and the ratio of two of the sides of the triangle.

Whereby, the inscribing figure of the quadrilateral is a regular hexagon, we get;

Interior angle of a regular hexagon = 120°

The 10 cm segment bisects the top vertex angle of the regular hexagon, which together with the 5·√3 cm side and trigonometric ratios, indicates that we get;

sin(60) = s/(5·√3) = (√3)/2

Where;

s = The side length of the regular hexagon

(5·√3)/s = (√3)/2

s = (5·√3)/((√3)/2) = 10

The side length of the regular hexagon, s = 10

The area of the regular hexagon, A = ((3·√3)/2) × s² = (1/2)×6 ×s ×a

Where;

a = The apothem = 5·√3

Therefore; A = ((3·√3)/2) × 10² = 150·√3

A  = (1/2)×6 ×10 × 5·√3 = 150·√3

Area of the quadrilateral = 4 × (1/2) × 5·√3 × 10 = 100·√3

Area of the shaded region = Area of the hexagon - Area of the quadrilateral

Therefore;

Area of the shaded region = 150·√3 - 100·√3 = 50·√3 ≈ 86.6

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