Two consecutive numbers exist such that the sum of three times the first number and two less than the second number is equal to 144. What are third numbers

Answer:

someone answer please ive been waiting for 2 hours :skull:

Step-by-step explanation:  please answer yall

Answer: The equation of the line that passes through the point negative -5, 7 and has a slope of -2/5 is y = -0.4x + 5.

We know that the store discounts 30% of the original price for an item, then, to calculate the discount we just have to multiply the original sell price by the discount percent and divide it by 100, like this:

Then, the discount is $109.5.

The new total would be the difference between the original price of the item and the discount, like this:

New price= $365-$109.5=$255.5

In order to find the confidence interval, follow these steps:

1. calculate the "p-hat" value, we can calculate it by dividing the number of people that said they have started paying bills online by the total number of people, like this:

p-hat = 1422/2767 = 0.51

2. Calculate the margin of error.

The margin of error "ME" is given by the following formula:

Where n is the sample size (2767 in this case) and z is the z-score value. The z-score is tabulated and it depends on the value of the confidence percentage, in this case we have a 99% confidence and the z-score is 2.5758 for this value, then we get:

3. Add and subtract the ME from the p-hat value, like this:

The confidence interval is determined by subtracting and adding the ME to the p-hat, then we get:

CI = (0.51 - 0.024, 0.51 + 0.024) = (0.486, 0.534)

Then, a 99% confidence interval for the population proportion is ​(0.486, 0.534)

The probability that Marshall wins a prize on his second spin =  0.1875

Consider an event X = the number of spins until Marshall wins a prize.

Given that a prize wheel with 4 segments of equal size, one of which is labeled winner.

So, the sample space n = 4

For given event x, the possible outcomes = 1

Using the formula of probability,

p = x/n

p = 1/4

p = 0.25

So, the probability of success p = 0.25

q = 1 - p

q = 1 - 0.25

q = 0.75

To find the probability that Marshall wins a prize on his 2nd spin.

Using formula, \(P(X = k) = (1 - p)^{k-1}p\)

For  k = 2,

\(P(X = 2) = (1 - 0.25)^{2-1}\times 0.25\)

P(X = 2) = 0.75 × 0.25

P(X = 2) = 0.1875

Thus, the required probability is  0.1875

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The probability of a even number less than 8 will be 3/10.

What is the definition of probability?

The possibility of an event is expressed by probability. This field of mathematics is concerned with the occurrence of a random event. The value varies from 0 to 1. In mathematics, probability is used to forecast the likelihood of occurrences occurring.

The potential of something happening is referred to as probability. The probability distribution makes use of this fundamental principle in probability theory. Before we can evaluate the likelihood of an event occurring, we must first know the total number of alternatives.

P(E) is the chance that an event will occur divided by the total number of outcomes.

Now,

Given sample space  S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

and Event E="Even number less than 8"

{2,4,6}

Then, Probability of event E=3/10

Hence,

          The probability of a even number less than 8 will be 3/10.

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Answer:

2291

Step-by-step explanation:

Given: Radius of a city's town hall is equal to 5-mile and about 180,000 people live in a city's town hall

To find: population density per square mile

Solution:

Population density refers to the number of people per unit of area.

Let r denotes radius of the town hall = 5 miles

Area of the town hall = \(\pi r^2=\pi (5)^2=25\,\pi\) square miles

Population density per square mile = Population of a city's town hall/area of the town hall = 2290.9 \(\approx 2291\)

According to the equation, values of "Y" in the table would be 10 if X is 4 ; 12 if X is 5 ; 18 if X is 8 and 20 if X is 9.

As given equation is "Y=2x+2"

According to the table, we will put values of X in the equation to find the value of Y.

When X = 4,

Y = 2×4 + 2

Y = 10

When X = 5

Y = 2×5 + 2

Y = 12

When X = 8

Y = 2×8 + 2

Y = 18

When X = 9

Y = 2×9 + 2

Y = 20

Therefore values of Y would be 10, 12, 18, and 20 when X is 4, 5, 8, and 9 Respectively.

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—------------- CORRECT QUESTION FORMAT IS GIVEN BELOW —-----------

(Q). Fill in the blank using this function Y=2x+2.

(Table is given below as in image section)

Answer:

B. The lower extreme increased.

Step-by-step explanation:

From the original box and whisker plot, the lower extreme (minimum) is 5 ; The upper extreme, maximum is 15.

The number of batches baked on the eight day is 20. This exceeds tbe previous maximum value. Hence, upper extreme( maximum) value of the new plot will change from 15 to 20.

The lower extreme isn't affected as the obtained value isn't below 5.

The median value will Increase and the upper quartile value will also increase. Once the upper quartile value increases, the interquartile range will also increase

The slope of a line parallel to the line whose equation 8x + 10y = 60 is -4/5

What is Equation of line ?

A straight line's general equation is y = mx + b, where m denotes the gradient or slope and y = b denotes the point at which the line crosses the y-axis. On the y-axis, this value b is referred to as the intercept.

Given the equation,

8x + 10y = 60

We know, the equation of line is in form of

y = mx + b

m = slope and b = y-intercept

Now, evaluate the given equation

8x + 10y = 60

10y = 60 - 8x

y = (60 - 8x) / 10

y = 60/10 - 8x/10

y  = 6 - 4/5x

y = -4/5x + 6

Which is in the form of equation of line

y = -4/5x + 6

Now, from this slope is - 4/5 and y-intercept is 6

Hence, the slope of a line parallel to the line whose equation 8x + 10y = 60 is -4/5

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Answer:

3/9

Step-by-step explanation:

3/9 because it goes up 3 right 9

There is a 0.022 percent chance that a student may receive a quiz grade of 95 or above.

The z-score formula is as follows:

z = (95-85)/8.0

= 1.25

Using the z-score table, calculate the probability:

P(z >= 1.25)

= 0.022

The z-score formula can be used to determine the likelihood that a student would receive a quiz grade of 95 or higher. The data set's mean and standard deviation are considered in the formula. The mean score on the quiz in this instance is 85, and the standard deviation is 8.0. By deducting the mean from the desired score (95), the z-score can be computed by dividing the result by the standard deviation (8.0). The z-score in this instance is 1.25.  The likelihood that a student will receive a quiz grade of 95 or higher can be determined using the z-score table. The likelihood of a z-score of 1.25 or higher is 0.022, according to the table. This indicates that there is a 0.022 percent chance that a student will receive a quiz grade of 95 or above.

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Answer:

The dotted line is 4.9

Step-by-step explanation:

The lower triangle is a right triangle so we can use the Pythagorean theorem

a^2+b^2 = c^2

where a and b are the legs and c is the hypotenuse

2^2 + 4^2 = c^2

4+16 = c^2

20 =c^2

Taking the square root of each side

sqrt(20) = c

The upper rectangle has a length of sqrt(20) and a height of 2

We can use the  Pythagorean theorem

a^2+b^2 = c^2

where a and b are the legs and c is the hypotenuse  to find the  diagonal

2^2 + (sqrt(20))^2 = c^2

4+20 = c^2

24 = c^2

Taking the square root of each side

sqrt(24) = c

4.898979486=c

Rounding to the nearest tenth

4.9 =c

In an expression using the logical operator And Also, as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false.

The And Also operator is a short-circuiting operator that is used to combine two or more Boolean expressions. It evaluates the left-hand expression first and then the right-hand expression only if the left-hand expression evaluates to true

. If the left-hand expression evaluates to false, then the right-hand expression is not evaluated at all. This helps to improve the performance of the code by avoiding unnecessary evaluations of expressions that would not change the outcome of the overall condition.

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In an expression using the logical operator And Also , as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false. Therefore option c. And Also correct.

This is because the AndAlso operator employs short-circuit evaluation, meaning it stops evaluating once it encounters

the first false condition since the overall result will definitely be false.

In an expression using AndAlso, if the first condition is false, the entire expression is evaluated as false without testing

any further conditions. This is also known as short-circuit evaluation.

In contrast, the OrElse operator evaluates to true as soon as one of the compound conditions is true, without testing

any further conditions. The Nor and Xor operators are less commonly used and have different behavior.

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Answer:

I think ( b) is non proportional linear

Answer:

378 because 6×7 is 42 and 16×21 is 336 and them and get. 378

To determine the change in angular momentum (ΔL) of a cylinder from t = 0 to t = t0, a student can use the equation:

ΔL = I * Δω

where ΔL is the change in angular momentum, I is the moment of inertia of the cylinder, and Δω is the change in angular velocity.

To calculate Δω, the student needs to know the initial and final angular velocities, ω0 and ωt0, respectively. The change in angular velocity can be calculated as:

Δω = ωt0 - ω0

Once Δω is determined, the student can use the moment of inertia (I) of the cylinder to calculate ΔL using the equation mentioned earlier.

The moment of inertia (I) depends on the mass distribution and shape of the cylinder. For a solid cylinder rotating about its central axis, the moment of inertia is given by:

I = (1/2) * m * r^2

where m is the mass of the cylinder and r is the radius of the cylinder.

By substituting the known values for Δω and I into the equation ΔL = I * Δω, the student can calculate the change in angular momentum (ΔL) of the cylinder from t = 0 to t = t0.

It's important to note that this method assumes that no external torques act on the cylinder during the time interval. If there are external torques involved, the equation for ΔL would need to include those torques as well.

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Answer:

Solutions have 2 real roots.

Step-by-step explanation:

Discriminant determines the solutions of quadratic equation.

If the value of discriminant is greater than 0 or D > 0 or D is positive then there are 2 real roots.

If the value of discriminant is 0, there is one real root.

If the value of discriminant is less than 0 or in negative then there are no real roots.

Formula

Discriminant can be found using:

\( \displaystyle \large{D = {b}^{2} - 4ac}\)

The discriminant derives from Quadratic Formula.

\( \displaystyle \large{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }\)

Now you should know why D > 0 gives 2 real roots because of ± which determines 2 solutions.

D = 0 gives one real root because x would be -b/2a

D < 0 gives no real roots because in square root, the value is negative which does not exist in real number.

Answer:

y = -1/2x

Step-by-step explanation:

If two lines are perpendicular to each other, they have opposite slopes.

The first line is y = 2x + 5. Its slope is 2. A line perpendicular to this one will have a slope of -1/2.

Plug this value (-1/2) into your standard point-slope equation of y = mx + b.

y = -1/2x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (-4, 2). Plug in the x and y values into the x and y of the standard equation.

2 = -1/2(-4) + b

To find b, multiply the slope and the input of x (-4)

2 = 2 + b

Now, subtract 2 from both sides to isolate b.

0 = b

Plug this into your standard equation.

y = -1/2x + 0 or y = -1/2x

This equation is perpendicular to your given equation (y = 2x + 5) and contains point (-4, 2)

Hope this helps!

The answer  is that the quadratic function is the one that models the situation.

The function that models the situation is a quadratic function in the form of ax² + bx + c.

In this scenario, the engineer is designing a flashlight with a parabolic mirror. A parabolic mirror has a shape that can be represented by a quadratic function. Quadratic functions are typically in the form of f(x) = ax² + bx + c, where a, b, and c are constants.

The explanation for this is that a parabolic mirror reflects light in a way that the reflected rays converge at the focus, which is the vertex of the parabola. This means that the distance between the reflector and the light source should be the same as the distance between the reflector and the focus. The shape of the parabolic mirror is defined by a quadratic function, which is y = ax²

The variable y represents the height of the mirror at a given point, x represents the distance from the vertex, and a is a constant that determines the steepness of the curve. Therefore, the engineer can use this equation to design the parabolic mirror that will maximize the output of the flashlight.
.

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The solution is, B) yes; -2/3, i.e. a proportional relationship exists & -2/3  is the constant ratio of y/x .

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

if it is proportional

then.,

y = kx

so, we get,

-2 = 3 k ⇒ k= (-2/3)

-4 = 6 k ⇒ k= (-2/3)

-8 = 12k ⇒ k= (-2/3)

Hence, The solution is, B) yes; -2/3, i.e. a proportional relationship exists & -2/3  is the constant ratio of y/x .

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Answer:

158962.5

Step-by-step explanation:

it is already round to the tenth ,but if you are talking about rounding to the neartest whole number is it 158963

sorry if i am wrong :) have a nice day

In order to go from figure 1 to figure 2, there are a number of different transformations that can be selected.

First, notice that figure 2 is exactly three times as large as figure 1, therefore, there has been a dilation by a factor of three (3) that took place .

So Let's say that we do the dilation first.

Step 1: Dilation by a factor of "3" using the point (-1, -2) which is one of the vertices of the triangle, for reference. Then, the new triangle would have new coordinaes for the vertices at the points:

(-1, -2) (-1, 1) and (-6, -2)

I am making a drawing to show the change (give me a little time)

So, we see that the dilated triangle is represented by the green one in the image above.

Step 2: we are now going the "reflect the green triangle around the horizontal line y = 2 represented by the blue line . When we reflect the green triangle around that line, we obtain the orange triangle.

Step 3: we are going to do another reflection, this time a reflection around the vertical line x = 1 (noted in purple in the image above). After this, we obtain the triangle in figure 2.

So we

The solution to the equation does not exist

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

2x - 3 = 0

2x - 3 = 3

Also from the question, we understand that the graph is given as

3 = 0

The above equation is false, and cannot be represented on a graph

This is so because 0 and 3 do not have the same value

Similarly, we have 2x - 3 = 0 and 2x - 3 = 3

By substitution, the equations becomes

0 = 3

Hence, the equation has no solution

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Complete question

Graph of 3=0

Solve the equation 2x - 3 = 0 and 2x - 3 = 3 graphically

The highest point of the arch is 9/10 feet above the ground.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

To find the highest point of the arch, we need to find the vertex of the parabola defined by the function h = -1/5x²+x.

The vertex of a parabola represented by the equation y = ax² + bx + c is given by

(-b/2a, c-b²/4a)

The vertex of the parabola is given by (-1/2×1/5, h-1/4×1/25) = (1/10, h-1/100)

Now substitute the value of h from the given equation:

h=-1/5x²+x

So, the value of h at the vertex is (1/10, -1/5 × (1/10)²+1/10-1/100) = (1/10, 9/100)

Thus, the highest point of the arch is 9/10 feet above the ground.

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The correct value of "x" is equal to 4

Step-by-step solution:

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

Using Pythagoras's Theorem:-

\((Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2}\)

\((x+1)^{2} -x^{2} =3^{2}\)

\((x+1)^{2} -x^{2} =3^{2}\)

\((x+1+x)(x+1-x) =3^{2}\)

\((2x+1)(1) =3^{2}\)

\((2x+1)(1) =9\)

\((2x+1) =9\\2x=9-1\\2x=8\\x=4\\\)

Therefore, the value of "x" is: x=4

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The value of the 6 in the ten-thousands place is 10,000 times greater than the value of the 6 in the tens place.

In Mathematics and Geometry, a place value is a numerical value (number) which denotes a digit based on its position in a given number and it includes the following:

6 in the ten-thousands = 60,000

6 in the tens place = 60

Value = 60,000/60

Value = 10,000.

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