Solve for x.
x + 7x =64

The largest number that divides two or more numbers evenly is greatest common divisor (GCD).

The biggest positive number that divides any non-zero integer by two or more is known as the greatest common divisor.

The greatest common divisor is the biggest number that divides two or more numbers proportionally (GCD).

Using the LCM method, the steps to calculate the GCD of (a, b) are as follows:

Find the result of a and b in step 1.

Find a and b's least common multiple (LCM) in step two.

Step 3: Dividing the results of Steps 1 and 2.

Step 4: The value that results from division is the most significant common divisor of (a, b).

To know more about greatest common divisor (GCD) visit,

brainly.com/question/1535295

#SPJ4

Area between each score and the mean in the z score table and then subtract the smaller area from the larger area.

The correct option is b.

The area between each score and the mean in the z score table and then subtract the smaller area from the larger area.

What is Z score: The z-score (aka, standard score) is a dimensionless metric that represents the deviation of a score from the mean in units of the standard deviation.

The formula for computing z-scores is as follows:

Z = (X - μ) / σ

where X is the score,

μ is the mean,

and σ is the standard deviation.

Z-scores can be used to assess the relative position of a score in relation to the distribution's mean and standard deviation.

In this particular question, the Z score of two test scores is 1.2 and 1.5.

To obtain the area between these scores, we have to find the area between each score and the mean in the z-score table, and then subtract the smaller area from the larger area.

First, we need to find the area between 1.2 and 1.5.

We can see the area from the z-score table as P(z < 1.5) - P(z < 1.2).

The following z-score table can be used to find these probabilities:

z-score table

From the table, P(z < 1.5) is equal to 0.9332, and P(z < 1.2) is equal to 0.8849.

Thus, P(1.2 < z < 1.5) = 0.9332 - 0.8849 = 0.0483.

To find the answer to the question, we have to calculate the area between the scores, which is 0.0483 in this case, by finding the area between each score and the mean in the z-score table and then subtracting the smaller area from the larger area.

For similar question on z score.

https://brainly.com/question/30892911

#SPJ11

The function f(x, y) =\(x^3 + y^3 + 9x^2 - 3y^2 - 4\) has a local maximum at (-3/2, 0). The local maximum value is -22.75.

To find the local maxima, local minima, and saddle points of the function f(x, y), we need to determine the critical points where the partial derivatives of f with respect to x and y are zero or undefined. Let's calculate these partial derivatives:

∂f/∂x = \(3x^2 + 18x\)

∂f/∂y = \(3y^2 - 6y\)

Setting these derivatives equal to zero and solving for x and y, we find that x = -3/2 and y = 0 are the critical points. To determine the nature of these critical points, we can use the second partial derivative test.

Calculating the second partial derivatives:

∂²f/∂x² = 6x + 18

∂²f/∂y² = 6y - 6

∂²f/∂x∂y = 0

At the critical point (-3/2, 0), we have ∂²f/∂x² = 6(-3/2) + 18 = -9 and ∂²f/∂y² = 6(0) - 6 = -6. Since the determinant of the Hessian matrix (∂²f/∂x² * ∂²f/∂y² - (∂²f/∂x∂y)^2) is positive and ∂²f/∂x² is negative, (-3/2, 0) is a local maximum.

Therefore, the function f(x, y) = \(x^3 + y^3 + 9x^2 - 3y^2 - 4\) has a local maximum at (-3/2, 0), and the local maximum value is -22.75.

Learn more about function here:

https://brainly.com/question/30721594

#SPJ11

Answer:

The rate charged by first mechanic per hour= x =$85

The rat charged by second mechanic per hour =y = $70

Step-by-step explanation:

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1900. What was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour?

Solution

Let

x= hourly rate of the first mechanic

y= hourly rate of the second mechanic

Derive two equations to solve for the two unknowns

10x + 15y = 1900 (1)

x + y = 155 (2)

From (2)

x + y = 155

x=155-y

Substitute x=155-y into (1)

10x + 15y = 1900

10(155-y) + 15y =1900

1550 -10y + 15y =1900

5y =1900-1550

5y=350

Divide both sides by 5

y= 70

Substitute y=70 into (2)

x + y = 155

x + (70) =155

x=155 - 70

= 85

x= 85

The rate charged by first mechanic per hour= x =$85

The rat charged by second mechanic per hour =y = $70

The estimate for the number of cars that are red will be 9450000.

From the information, when Ben sat outside his school in Cambridge and made a note of the colour of the first 100 cars that passed, he found out that 27 of them were red.

Based on the above, the ratio of red cars to total cars is 27:100.

Therefore, if thee are 35 million cars, the red cars will be:

= Ratio of red cars × Total cars

= 27/100 × 3500000

= 9450000

The number of red cards is 9450000.

Learn more about ratio on:

brainly.com/question/2328454

#SPJ1

The probability that all the numbers in the sequence are even is:

12%.

According to the statement

We have given that the A lock is opened using a sequence of three numbers. The numbers range from 0 to 39, inclusive, and cannot be repeated within the sequence. And we have to find the probability that all the numbers in the sequence are even.

So, For this purpose we know that the

Probability is the chance that a given event will occur.

So,

According to the given information it means that the

This means that there are total 20 even numbers.(0,2,4,6,.....,38)

and 20 odd numbers (i.e. 1,3,5,....,39)

Hence, the probability that all the numbers in the sequence are even is calculated as:

=20/40 * 19/39 * 18/38

= 3/26.

( Since, in the first place we have total 20 choices out of 40 numbers.

in the second place as one number has been chosen and there is no repetition hence we have 19 choices out of 39 numbers and similarly for the third place we have 18 choices out of the 38 available numbers)

Hence, in percentage the probability is given as:

Percentage = 3/26*100

Percentage = 11.53%

To the nearest whole number it is 12%.

Hence, the probability that all the numbers in the sequence are even is:

12%.

Learn more about Probability here

https://brainly.com/question/24756209

#SPJ4

A higher percentage of people who did not wear wrist guards (41.67%) experienced wrist injuries compared to those who did wear wrist guards (11.32%).

Based on the information provided, we can analyze the data on injuries to in-line skaters. Let's break down the given numbers:

Total number of people interviewed: 161

Number of people wearing wrist guards: 53

Number of people wearing wrist guards with wrist injuries: 6

Number of people not wearing wrist guards: 108

Number of people not wearing wrist guards with wrist injuries: 45

From this information, we can calculate the following:

Percentage of people wearing wrist guards with wrist injuries:

(Number of people wearing wrist guards with wrist injuries / Number of people wearing wrist guards) × 100

= (6 / 53)× 100 ≈ 11.32%

Percentage of people not wearing wrist guards with wrist injuries:

(Number of people not wearing wrist guards with wrist injuries / Number of people not wearing wrist guards)×100

= (45 / 108) ×100 ≈ 41.67%

These calculations provide insights into the likelihood of wrist injuries in relation to wearing wrist guards while inline skating. The data suggests that the percentage of wrist injuries among those wearing wrist guards is lower (11.32%) compared to those not wearing wrist guards (41.67%). This indicates that wearing wrist guards may offer some protection against wrist injuries while inline skating.

Learn more about percentage here:

https://brainly.com/question/843074

#SPJ11

The time to calculate her rate along the summit Rate = 1.5 mph

Rate = Distance / Time

To solve this problem, we will first need to calculate the time it took Jane to reach the peak. Since she rode 40 miles uphill, we can use the rate of 5 mph slower than when she reached the peak to calculate this time.

Time = Distance / Rate

Time = 40 miles / (Rate - 5 mph)

Time = 40 miles / (Rate - 5 mph)

Time = 40 miles / (Rate - 5)

Time = 8 hours

Since Jane spent 2 hours exploring the mountain, the total time it took her to reach the peak was 8 hours. We can now use this time to calculate her rate along the summit.

Rate = Distance / Time

Rate = 12 miles / 8 hours

Rate = 1.5 mph

Learn more about total time here:

https://brainly.com/question/951637

#SPJ4

Answer:

  -4.697 in/s

Step-by-step explanation:

You want to know the rate of change of radius of a cone 11 inches high with a radius of 5 inches and a volume that is decreasing at the rate of 541 cubic inches per second.

The volume of a cone is given by ...

  V = π/3r²h

The rate of change is found by implicit differentiation:

  V' = (π/3)((2rr')h +r²h')

Here, the height is constant, so h' = 0. Solving for r', we find ...

  r' = 3V'/(2πrh)

Using the given values of V', r, and h, we find the rate of change of radius to be ...

  r' = 3(-541 in³/s)/(2π(5 in)(11 in)) = -1623/(110π) in/s ≈ -4.69652 in/s

The radius is decreasing at about -4.697 inches per second.

__

Additional comment

The initial radius of the cone is irrelevant to the problem, since we want to know the rate of change at a specific different radius. Whether the cone is inverted or not is also irrelevant to its volume.

Jared bought 7 cans of paint. Let the number of red paint cans that Jared bought be x. The number of black paint cans he bought would be 7 - x. A can of red paint costs $3.75 and a can of black paint costs $2.75.

He spent $22 in all. Therefore we can write:3.75x + 2.75(7 - x) = 22 Multiplying out the second term and collecting like terms gives:0.5x + 19.25 = 22Subtracting 19.25 from both sides:0.5x = 2.75Dividing by 0.5:x = 5.5Since Jared can't buy half a can of paint, we should round the answer to the nearest integer. Hence, he bought 5 cans of red paint and 2 cans of black paint. The total cost of the 5 cans of red paint would be 5 x $3.75 = $18.75.The total cost of the 2 cans of black paint would be 2 x $2.75 = $5.50.The total cost of all 7 cans of paint would be $18.75 + $5.50 = $24.25.We spent more than Jared's budget. The value of $24.25 exceeds Jared's budget of $22. Hence, there is a problem with this problem statement.

Learn more about the number here:

https://brainly.com/question/24627477

#SPJ11

Answer:

Step-by-step explanation:

a:) Solve for b:

a = b/c^2

a = b/c^2 is equivalent to b/c^2 = a:

b/c^2 = a

Multiply both sides by c^2:

Answer: b = a c^2 = Dark Green

part 2) a = b/c^2 where a = 1/8, c = 4

b = 2

____________________________________________

b:) Solve for v:

-v + m = k

Subtract m from both sides:

-v = -m + k

Multiply both sides by -1:

Answer: v = m - k = Light blue

part 2) m - v = k where k = -7, m = -2

v = 5

__________________________________________

c:) Solve for q:

p/q = r/s

Take the reciprocal of both sides:

q/p = s/r

Multiply both sides by p:

Answer: q = (p s)/r = yellow

part 2) p/q = r/s where p = 14, r = -7, s = -4

q = 8

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.T

o find the value of x, follow these steps:

Step 1: Add the given probabilities.
(5/12) + (1/12) + (1/4) = (5/12) + (1/12) + (3/12) = (9/12)

Step 2: Since the probabilities must add up to 1, subtract the sum of the given probabilities from 1.
1 - (9/12) = (12/12) - (9/12) = 3/12

Step 3: Simplify the fraction, if necessary.
3/12 can be simplified to 1/4 by dividing both the numerator and denominator by 3.

So, the value of x is 1/4.

Your answer: A. 1/4

To learn more about Probability : brainly.com/question/11234923

#SPJ11

Answer:

1020 handshakes including the bride and the groom. 980 excluding the groom and the bride.

Step-by-step explanation:

(20*19) twenty people on the brides side shake hands with the other 19 people (19 because you can't really shake your own hand).

+(20*30) twenty people on the brides side shake hand with 30 people on the grooms side.

+(20*2) twenty people on the brides side shake hands with the bride and the groom.

this equalssss......

1020!!!!

Since the grooms family does hugs instead of handshakes, you'd only calculate how many the brides side does.

Answer:

Step by step explanation:

Since the triangles ALX and GIW are congruent, they have the same angles.

Then, if they are congruent:

Answer:

the one on the left

Step-by-step explanation:

The measure of the acute base angle is 69°

The measure of the obtuse base angle is 111°

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Isosceles triangles mean two sides are equal and the angles opposite to the equal sides are also equal.

Now,

Isosceles trapezoid

Vertex angle = 42

This means,

The other two angles will be the same.

x + x + 42 = 180

2x = 180 - 42

2x = 138

x = 69

Now,

The opposite angles of an isosceles trapezoid are supplementary.

So,

Obtuse base angle + Acute base angle = 180

Obtuse base angle + 69 = 180

Obtuse base angle = 180 - 69 = 111

Thus,

Acute base angle = 69°

Obtuse base angle = 111°

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ1

Answer:

230

Step-by-step explanation:

23% of 45 = 10.35

10.35 / 4.5 = 2.3

2.3 x 100 = 230

Step-by-step explanation:

it will be equal 230 as in the shown photo

The Pythagorean theorem is a fundamental concept in geometry that relates the lengths of the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, it can be expressed as:

a² + b² = c²

where a and b are the lengths of the two legs of the right triangle, and c is the length of the hypotenuse.

The converse of the Pythagorean theorem states that if the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

The Pythagorean theorem is a powerful tool in solving problems involving right triangles. It allows us to calculate unknown side lengths or determine whether a triangle is a right triangle based on the lengths of its sides. It has numerous applications in various fields, including engineering, architecture, physics, and navigation.

Understanding the Pythagorean theorem and its converse is essential for working with right triangles and applying geometric principles. It provides a foundation for further exploration of trigonometry and advanced geometric concepts.

To know more about Pythagorean theorem refer here:

https://brainly.com/question/28361847#

#SPJ11

The difference between exponential and quadratic function is variable exponent and base, shape of graph, y-intercept and rate of change of function of both.

The most basic difference evident in the equation is exponential function has variable exponent while quadratic function has base as variable. In this equation, the variable exponent is x written as power 1.03. The quadratic function has base x written with exponent 2. The exponential and quadratic function differ in exponential and parabolic growth.

Also, the rate of change in exponential function will increase with x. The quadratic function will alter according to the value x. The y-intercept is 2 for stated exponential function and 0 for given quadratic function f(x) = 2x².

Learn more about exponential function -

https://brainly.com/question/2456547

#SPJ1

Answer:

P>5hours

Step-by-step explanation:

practice time is > five hours

Answer:

you need to add up 430,516 x 817 and see what it gives you for my exclusive seen 1247.516

Step-by-step explanation:

Given that three charges (-25 nC, 79.1nC, and −55.9nC) are placed at three of the four corners of a square with sides of length 22.2 cm. We need to determine the value of the electric potential (in V) at the empty comer if the positive charge is placed in the opposite corner.

The formula for the electric potential at a point in space is given by;V = k [ (q1 / r1) + (q2 / r2) + (q3 / r3) + ….. ]where;k = Coulomb's constant (8.99 × 10^9 Nm²/C²)q1, q2, q3,…. are the charges at the cornersr1, r2, r3,…. are the distances from the corner to the point whose potential is being calculated Now we can calculate the electric potential at the empty corner as follows;The three charges can be represented as shown below:Charges at corners of a square

The distance from any corner to the opposite corner (where the positive charge is placed) is given by d = √[ (22.2 cm)² + (22.2 cm)² ] = 31.4 cmTherefore, the electric potential at the empty corner is given by;V = k [ (q1 / r1) + (q2 / r2) + (q3 / r3) ]Here, q1 = -25 nC, q2 = -55.9 nC, q3 = 79.1 nC, r1 = r2 = r3 = d = 31.4 cm = 0.314 mPlugging in the values we get;V = 8.99 × 10^9 [ (-25 × 10^-9 / 0.314) + (-55.9 × 10^-9 / 0.314) + (79.1 × 10^-9 / 0.314) ]= 8.99 × 10^9 [ -0.0795 - 0.1783 + 0.252 ]= 8.99 × 10^9 × 0.0052= 46.8 VTherefore, the value of the electric potential at the empty comer if the positive charge is placed in the opposite comer is 46.8 V.

To know more about square visit:

https://brainly.com/question/14198272

#SPJ11

They needed a total of 8 weeks to save the same amount of money, and after 8 weeks, everyone would have $200.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Harper and Joe want to buy season passes for Disneyland but neither of them has the $1,300 needed to purchase a pass.

Since Harper decides to get a job that pays $25 a week. She has nothing saved right now. Joe already has $80 and plans to save $15 of her weekly allowance.

To save up for the season pass:

Harper needs = 1300$

Since, She earns 25$ a week

Harper needs total weeks = 1300/25

Harper needs total weeks = 52 weeks

joe also needs 1300 $

Since, joe already has $80 and plans to save $15 of her weekly allowance.

Joe needs total weeks = (1300 -80)/15

Joe needs total weeks = 81.33

To have the same amount of money saved up:

Let "x" be the weeks they required to save the equal money:

25 *x = 80 + 15*x

10*x = 80

x = 8

Everyone will have = 25 * 8

Everyone will have = 200$

Therefore, they required total of 8 weeks to have the same amount of money saved up and everyone will have 200$ after 8 weeks.

Learn more about Mathematical operations here:

https://brainly.com/question/20628271

#SPJ1

The reflected and then translated coordinates of the triangle are R'( 3,2), S'(3,5), and T'( 8, 5).

A sort of symmetry known as reflective symmetry occurs when one half of an object mirrors the other half. It also goes by the name "mirror symmetry."

For instance, both the left and right sides of a human face are typically the same. Most butterflies have identical wings on their left and right sides.

The given points of the triangle are R(3,-4), S(3,-7), and T(8,-7).

The reflected points of the triangle will be:-

R(3,-4) = R'( 3, 4)

S(3,-7) = R'(3,7)

T(8,-7) = R(8, 7)

The translated points by 2 units down will be:-

R'( 3, 4) = R''( 3, 2)

R'(3,7) = S''( 3, 5)

R(8, 7) = T''(8,5)

Therefore, the reflected and then translated coordinates of the triangle are R'( 3,2), S'(3,5), and T'( 8, 5).

To know more about translation follow

https://brainly.com/question/1574635

#SPJ1

Answer:

so the other guy can get brainlyest

Step-by-step explanation:

pls like and rate

item (a):

Using the formula given in the question, we have

Our principal investment P is equal to $4000, our interest r is 3 1/4 %, writting this in decimal form we have

Since it is a percentage, to write in decimal we divide by 100

And finally, our n value is 365 since it is compounded daily, and we have 365 days in a year.

Then, our function is

item (b):

To find A(30), we just need to evaluate this value in the function we created before

This means that with an investment of $4000, with this rate Joe is going to have a return of $10604.21.

Answer:

317

Step-by-step explanation:

2(5-(-3))² + 7(-3)

2(5+8)² + (-21)

2(13)² - 21

2(169) - 21

338 - 21 = 317

The elasticity of demand for the given garden shop's demand function is [-95P(20x+9)^3] / [(5x+300)^2 × (19x+9)].

To find the elasticity of demand, we need to use the following formula

E = (P/Q) × (dQ/dP)

Where E is the elasticity of demand, P is the price, Q is the quantity demanded, and (dQ/dP) is the derivative of the demand function with respect to price.

Given the demand function: q = D(x) = (5x+300) / (20x+9)

To find (dQ/dP), we first need to find (dq/dx) as follows

dq/dx = d/dx [(5x+300)/(20x+9)]

= [(20x+9)(5) - (5x+300)(20)] / (20x+9)^2

= - 475x - 4500 / (20x+9)^2

Next, we use the chain rule to find (dQ/dP)

dQ/dP = dQ/dx × dx/dP

= (dq/dx) × (-1 / (20x+9)^2)

Substituting the value of (dq/dx), we get

dQ/dP = [-475x - 4500] / [(20x+9)^2 × (20x+9)]

Now, we can find the elasticity of demand at a given price, say P

E = (P/Q) × (dQ/dP)

= (P/q) × [-475x - 4500] / [(20x+9)^2 × (20x+9)]

= [(P × (20x+9)^2 × (20x+9)) / (5x+300)] × [-475x - 4500]

We can simplify this expression further by substituting the value of q with the given demand function

E = [(P × (20x+9)^2 × (20x+9)) / ((5x+300) × (5x+300 + 15x))] × [-475x - 4500]

= [-95P(20x+9)^3] / [(5x+300)^2 × (19x+9)]

Learn more about elasticity of demand here

brainly.com/question/28945373

#SPJ4

The given question is incomplete, the complete question is:

A garden shop determines the demand function q = D(x) = 5x+300 / 20x+9 during early to me parts where are the number of cod per day when the prices des per Summer. Find the elasticity.

The area of the top surface of the wedge is approximately 9.97 square inches.

To find the area of the top surface of the wedge, we need to calculate the area of the corresponding sector of a circle.

The formula to calculate the area of a sector is:

Area = \((θ/2) * r^2\)

Where:

θ is the central angle (in radians)

r is the radius of the circle

In this case, the central angle is π/4 and the radius is 3 inches.

Plugging in the values into the formula:

Area =\((π/4 / 2) * (3 inches)^2\)

Simplifying:

Area = (π/8) * 9 square inches

Approximating the value of π to 3.14:

Area ≈ (3.14/8) * 9 square inches

Area ≈ 1.10775 * 9 square inches

Area ≈ 9.96975 square inches

Therefore, the area of the top surface of the wedge is approximately 9.97 square inches.

For such more questions on Wedge Surface Area

https://brainly.com/question/26666857

#SPJ11

Step-by-step explanation:

the process is shown above hope you understand.