find three consecutive integers such that four times the first added to the third is 92
SOLVE QUICKLY
Thanks​

Answer:  7/24 ≅ 0.2916667

Step-by-step explanation: QUICK MATH

The time takes by car to cover the distance between two cities by car varies inversely with the speed of car. Total 5 hours will consume to complete the trip with a car moving at 40 mph.

Time is taken in traveling a particular distance is proportional to the distance traveled which means more distance covered in more time.

The speed of an object is defined as the 'distance traveled per unit time'. Formula is written as [tex]Speed(s ) = \frac{Distance(d)}{Time(t)}[/tex]

Now, Speed of car (s) = 50 miles per hour

Car takes 4 hours to complete the trip. Let the distance travelled by car in 4 hour during the trip be 'x'. Applying the speed formula, [tex]50 mph = \frac{ x}{4 \: \: hours}[/tex]

=> x = 4 × 50 miles

=> x = 200 miles

Now, if the speed of car (s') = 40 mph in the trip. We have to determine the time taken by car to complete the trip with 40 mph speed. So, we know the speed of car and total distance travelled by car on trip. Using the time formula,[tex]time ( t') = \frac{distance (x) }{ speed( s')} [/tex]

=> [tex] time (t') = \frac{ 200 \: miles}{ 40 \: mph}[/tex]

= 5 hours.

Hence, required value of time is 5 hours.

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Complete question :

The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes four hours for a car moving at 50 mph. How long does the trip take for a car moving at 40 mph?

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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The scale factor that takes triangle C to triangle D is 3/10.

Scale factor is a number by which the size a geometrical figure or shape can be changed with respect to its original size.

To find the scale factor that takes triangle C to triangle D, we use the formula below

Formula:

Where:

From the diagram in the question,

Given:

Substitute these values into equation 1

Hence, the scale factor is 3/10.

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If the  volume of a volleyball is approximately 113 in³, then the diameter of the volleyball is approximately option (D) 5 inches.

The formula for the volume of a sphere is

V = (4/3)πr³

where V is the volume, π is pi (approximately 3.14), and r is the radius of the sphere.

We are given the volume of the volleyball as 113 in³, so we can solve for the radius as follows

113 = (4/3)πr³

r³ = 113 / ((4/3)π)

r³ ≈ 21.50

r ≈ 2.8

To find the diameter, we double the radius:

d = 2r ≈ 5.6

Rounding this to the nearest whole number

d = 5 in

Therefore, the correct option is (D) 5 in

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The solutions to the equation x² + 6x - 41 = 6x - 5 are x = 6 and x = -6.

To solve for all values of x by factoring x² + 6x - 41 = 6x - 5, we can first simplify the equation by combining like terms:

x² + 6x - 41 = 6x - 5

x² - 41 = -5

Next, we can bring all the terms to one side of the equation:

x² - 41 + 5 = 0

x² - 36 = 0

Now we can factor the left side of the equation:

(x - 6)(x + 6) = 0

Setting each factor equal to zero and solving for x, we get:

x - 6 = 0 or x + 6 = 0

x = 6 or x = -6

Therefore, the solutions to the equation x² + 6x - 41 = 6x - 5 are x = 6 and x = -6.

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Answer:

The vertices of the image after rotating triangle uvw 90 degrees counterclockwise are u′(0, −2), v′(1, −3), w′(3, −3).

Step-by-step explanation:

Step-by-step explanation:

For intersecting chords, the products of the related segments are equal

8 * 6   =     3x * x

48 = 3x^2

16 = x^2

x = 4   units

Answer:

a = 2

b = 4

c = 4.47

Step-by-step explanation:

a is 2 units long

b is 4 units tall

To find c, we can use the formula: a^2 + b^2 = c^2

Plug it in:

(2)^2 + (4)^2 = c^2

4 + 16 = c^2

20 = c^2

c = 4.47

Answer:

length a is 2 length b is 4 length c is 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

The absolute value (or modulus) | 5 - 3x | of a real number  5 - 3x is the non-negative value of 5 - 3x without regard to its sign.

| 5 - 3x| + 2 = 19

| 5 + 3x | = 19 - 2

| 5 + 3x | = 17

Ans: D

The Riemann sum that represents the illustration on the graph is the second option as i goes from 1 to 4:

[tex]1∑2 {(xᵢ)}^{2} [/tex]

The Riemann sum is a mathematical concept used to approximate the area under a curve. It is named after the German mathematician Bernhard Riemann.

The idea behind the Riemann sum is to divide the area under the curve into a series of rectangles, where the height of each rectangle is determined by the function being integrated, and the width of each rectangle is determined by the size of the intervals used to divide the domain of the function. The area of each rectangle is then calculated and added together to get an approximation of the total area under the curve.

The Riemann sum is written in the following form:

[tex]∑f(xᵢ)Δxᵢ[/tex]

where f(xᵢ) is the value of the function at the ith point in the interval, Δxᵢ is the width of the ith rectangle, and the sum is taken over all i intervals.

Thus, the Riemann sum that represents the illustration on the graph as i goes from 1 to 4 is:

[tex]1∑2 {(xᵢ)}^{2} [/tex]

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we get the velocity of the car at the end of the drag race to be 162 mph.

Assuming you meant "weight," weight is the measure of the amount of force that gravity exerts on an object. It is usually measured in units such as pounds or kilograms. The weight of an object can vary depending on the strength of gravity and the mass of the object. For example, an object that has a mass of 10 kilograms on Earth would weigh approximately 98 Newtons (which is about 22 pounds) due to the gravitational force of the Earth.

To find the velocity of the car, we can simply plug in the given values of horsepower and weight into the given formula:

[tex]v = 234 * \sqrt(p / w)[/tex]

Substituting p = 1311 and w = 2744, we get:

[tex]v = 234 * \sqrt(1311 / 2744)[/tex]

[tex]v \approx 162[/tex]

Rounding this to the nearest whole number, we get the velocity of the car at the end of the drag race to be 162 mph.

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Yes,  indicate that, on average, children tend to have more REM sleep than adults.

We can determine this by performing a two-sample t-test using the following null and alternative hypotheses:

Using a significance level of 0.01 and the given information, we calculate the t-statistic as follows:

t = ((2.8 - 2.1) - 0) / sqrt((0.5^2 / 10) + (0.7^2 / 10))

t = 2.697

Using a t-distribution table with degrees of freedom equal to 18 (10 + 10 - 2), we find the critical value to be 2.878 (for a one-tailed test at the 0.01 level of significance).

Since our calculated t-statistic of 2.697 is less than the critical value of 2.878, we fail to reject the null hypothesis.

Therefore, we conclude that there is evidence to suggest that children have more REM sleep than adults on average.

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Answer:

[tex]\frac{24\sqrt{5} }{5}[/tex]

Step-by-step explanation:

Let's start by assigning one of the unknown legs with the variable x.

We know that the other leg is 2 times the length of x, so we can write:

2x

We also know that the length of the hypotenuse is 12.

From here, we can use the Pythagorean Theorem.

Recall that the Pythagorean Theorem is:

[tex]a^2+b^2=c^2[/tex]

where a is the length of one leg, b is the length of the other leg, and c is the length of the hypotenuse.

Let's substitute the values. We have:

[tex]x^2+(2x^2)=12^2=\\x^2+4x^2=144=\\5x^2=144=\\x^2=\frac{144}{5}=\\x=\frac{12}{\sqrt{5} }[/tex]

Let's rationalize the denominator by multiplying the numerator and denominator by [tex]\sqrt{5}[/tex], like so:

[tex]\frac{12}{\sqrt{5} } =\\\frac{12\sqrt{5} }{5}[/tex]

Therefore, [tex]x=\frac{12\sqrt{5} }{5}[/tex]

Let's solve for 2x:

[tex]2x=\\2(\frac{12\sqrt{5} }{5})=\\ \frac{24\sqrt{5} }{5}[/tex]

So, the length of the longest leg is [tex]\frac{24\sqrt{5} }{5}[/tex]

The probability of getting a 5 or a divisor of 16 when spinning the spinner is 1/2 or 50%.

To find the probability of getting a 5 or a divisor of 16, we need to first understand what the spinner looks like. Assuming that the spinner has equally sized sections labeled 1 through 8, we can see that a divisor of 16 would be either 1, 2, or 4.

So, out of the eight possible outcomes, there are three that are divisors of 16 (1, 2, and 4) and one that is a 5. Therefore, there are four possible outcomes that satisfy the condition of getting a 5 or a divisor of 16.

To calculate the probability of getting a 5 or a divisor of 16, we divide the number of favorable outcomes (4) by the total number of possible outcomes (8). This gives us:

P(5 or divisor of 16) = favorable outcomes / total outcomes

= 4/8

= 1/2 or 50%

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The period of a cosine function of the form y = cos bx is equal to T= 2π/b where 'T' is the period of the cosine function and b is the coefficient of x in the function.

This formula tells us that the period of the cosine function is equal to the length of one complete cycle of the function.

it represents  the distance along the x-axis for the cosine function to complete one full oscillation.

The period of a cosine function of the form y = cos bx, first identify the coefficient b.

Use the formula T= 2π/b  to calculate the period 'T'.

For example,

Consider cosine function y = cos 2x,

The coefficient of x is 2.

Using the formula above, the period is equal to

Period = 2π/2

           = π

So the period of the function y = cos 2x is π.

This implies that the cosine function completes one full oscillation every π units along the x-axis.

Therefore, the formula used to calculate the period of the cosine function y = cos bx is given by T= 2π/b.

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Since the statement p(n) holds true for n = 1, we have successfully completed the basic step of the proof.

To complete the basic step of the proof, we need to show that the statement p(n) is true for the smallest positive integer n, which is 1.

Let's plug n = 1 into the statement p(n):[tex]1^3 = (\frac{1(1 + 1))}{2})^2[/tex]

Simplifying the equation, we get:
[tex]1^3 = (1(2)/2)^2\\1^3 = (1^2)^2\\1 = 1[/tex]

Since the statement p(n) holds true for n = 1, we have successfully completed the basic step of the proof.

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The statement is true for n=1, and we have completed the basis step of the proof.

To complete the basis step of the proof for the statement p(n), we need to show that it is true for the smallest positive

integer n, which is 1.

Our statement is:

[tex]1^3 + 2^3 + 3^3 + ... + n^3 = (n(n+1)/2)^2.[/tex]

For the basis step, let n = 1:

Left side: [tex]1^3 = 1[/tex]

Right side:[tex](1(1+1)/2)^2 = (1(2)/2)^2 = (1)^2 = 1[/tex]

Since the left side and the right side are equal, we have successfully completed the basis step of the proof for the statement p(n).

Therefore, the statement is true for n=1, and we have completed the basis step of the proof.

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We need at least 3.465 gallons of paint to paint the walls of this room.

The area of the two rectangular faces on either end of the prism is:

length x height = 17 x 12 = 204 square feet

The area of the two rectangular faces on the sides of the prism is:

width x height = 15 x 12 = 180 square feet

The area of the top and bottom faces of the prism is:

length x width = 17 x 15 = 255 square feet

The total surface area of the prism is:

2(204) + 2(180) + 2(255) = 1386 square feet

Now, we divide surface area by coverage of one gallon of paint:

1386 / 400 = 3.465

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Answer:

D: 27(12x² - 5x - 2).

Step-by-step explanation:

The formula for the surface area of a cylinder is: A = 2πr² + 2πrh

Given that the radius of the cylinder is 3x - 2 cm and the height is x + 3 cm, we can substitute these values in the formula and simplify:

A = 2π(3x - 2)² + 2π(3x - 2)(x + 3)

A = 2π(9x² - 12x + 4) + 2π(3x² + 7x - 6)

A = 18πx² - 24πx + 8π + 6πx² + 14πx - 12π

A = 24πx² - 10πx - 4π

A = 2π(12x² - 5x - 2)

Therefore, the answer is option D: 27(12x² - 5x - 2).

Answer:

D

Step-by-step explanation:

The standard definition of a quadratic function is given as follows:

y = ax² + bx + c.

The vertex is classified as a maximum or minimum depending on the term a, which multiplies x², as follows:

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The value of x for the given triangle through which the perimeter of the given relation is satisfied is 10.

What about perimeter of triangle?

The perimeter of a triangle is the total length of its boundary, which is the sum of the lengths of its three sides. The perimeter can be thought of as the distance around the triangle, and it is measured in units of length such as centimeters, meters, or feet. The perimeter of a triangle is an important geometric property that is used in many practical applications, such as calculating the amount of fencing needed to enclose a triangular-shaped garden or determining the length of wire required to form a triangular circuit.

According to the given information:

The perimeter of triangle is sum of all sides of the triangle

In which,

2x + 4 + 3x - 8 + x - 2 = 54

6x - 6  = 54

6x = 60

x = 10

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Answer: First choice 480t = 300t + 900

Step-by-step explanation:

A factory has two assembly lines, M and N, that make the same toy. On Monday, only assembly line M was functioning and it made 900 toys.  

On Tuesday, both assembly lines were functioning for the same amount of time. Line M made 300 toys per hour and line N made 480 toys per hour. Line N made as many toys on Tuesday as line M did over both days.

Write an equation that can be used to find the number of hours, t, that the assembly lines were functioning on Tuesday.

ANS

Let say t is time in hrs for Which Both Assembly line worked

M made 300 toys per hr on Tuesday

Toys made on Tuesday at Assembly line M = 300 × t  = 300t  toys

N made 480 toys per hr on Tuesday

Toys made on Tuesday at Assembly line N = 480 × t  = 480t  toys

Toys Made by N on Tuesday  = Toys made by M on Tuesday + Toys made by M on Monday

480t = 300t + 900

=> 180 t = 900

=> t = 900/180

=> t = 5 hr

N capacity on tuesday Per hour * t  = M capacity on tuesday per hour  * t  + Toys made by M on Monday

N = N capacity on tuesday Per hour

M = M capacity on tuesday Per hour

=> t (N - M ) = 900

=> t = 900/(N-M)

The probability that the man will hit his target at least once in 4 shots is calculated using the complementary probability of him missing all 4 shots. Since he hits his target 25% of the time, he misses it 75% of the time.

The probability of missing all 4 shots is (0.75)^4 = 0.3164.

Now, to find the probability of hitting the target at least once, subtract the probability of missing all shots from 1:

1 - 0.3164 = 0.6836 or 68.36%.

So, the probability that the man will hit his target at least once in 4 shots is approximately 68.36%.

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For the image with coordinates A'(3, 5), B'(3, -1) and C'(-2, 0) occurred after the x-axis refection.

The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).

The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).

Given data:

pre-image coordinates - A(3, -5), B(3, 1) and C(-2, 0).

Image coordinates A'(3, 5), B'(3, -1) and C'(-2, 0).

As its is clear from the given coordinates that value of x is same while the value of y gets change by negative.

(x,y) ---> (x, -y) , shows the refection about the x axis.

Thus, For the image with coordinates A'(3, 5), B'(3, -1) and C'(-2, 0) occurred after the refection about the x axis.

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Answer: 4

Step-by-step explanation:

Given:

   [tex]2log_62+3log_63+log_612[/tex]

Rewrite using the power property:

   [tex]log_62^2+log_63^3+log_612[/tex]

Rewrite by adding the logarithms together (multiplying) since they all have a common base of 6:

   [tex]log_6(2^2*3^3*12)[/tex]

Simplify by multiplying:

   [tex]log_6(4*27*12)[/tex]

   [tex]log_6(1,296)[/tex]

Evaluate the logarithm:

   [tex]log_6(1,296)[/tex]

   4

A. Talia can use 1 and 3/4 cup strawberries to double the recipe. B. Talia can use 1 and 1/3 cup yogurt to make 3 servings. D. Talia can use 2 cups orange juice to make 4 servings.

In statistics, a proportion is a fraction or a percentage that reflects the proportion of a population's or sample's members who share a particular attribute to the population's or sample's overall size. It is a kind of ratio where the denominator is the entire population or sample size and the numerator is the number of people who possess a specific trait or attribute.

From the given ingredients and the serving size we can see that the correct statement is:

A. Talia can use 1 and 3/4 cup strawberries to double the recipe.

B. Talia can use 1 and 1/3 cup yogurt to make 3 servings.

D. Talia can use 2 cups orange juice to make 4 servings.

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The complete question is:

Answer:

-34x+29

Step-by-step explanation:

[tex]7(5-x)-3(9x+2)=7.5-7x-3.9x-3.2=35-7x-27x-6\\=-34x+29[/tex]

The probability is 0.9835 where the sample mean would be greater than 59.5 kilograms.

The central limit theorem can be used to approximate the sampling distribution of the sample mean as a normal distribution.

where the mean equals the population mean (μ = 62 kg) and the standard deviation equals the population standard deviation divided by the square root of sample size (σ/sqrt (n) = sqrt(144 / 195) = 2.4287 kg).

Next, find the probability that the sample mean is greater than 59.5 kilograms.

z = (59.5 - 62) / (2.4287 / square (195)) = -2.1295

Using an ordinary regular table or calculator, we know that the probability of a Z-score less than -2.1295 is 0.0165.

Therefore, the probability that the sample mean exceeds 59.5 kilograms is

1 - 0.0165 = 0.9835

Rounding to four decimal places gives a probability of 0.9835.

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A scatter plot chart of stock returns versus past stock returns will typically appear as a random pattern mostly concentrated in the top-right and lower-left quadrants.

This pattern indicates that there is a positive correlation between past and current stock returns, but there are also instances where current returns are negative despite past positive returns.

The top-right quadrant represents instances where both past and current returns are positive, while the lower-left quadrant represents instances where both past and current returns are negative.

The random pattern indicates that stock returns cannot be predicted with certainty based on past returns alone.

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A congruence transformation that maps triangle RST to triangle UVW is a reflection along the line y = 1, followed by a translation 2 units right and down by 1 units.

A congruence transformation that maps triangle RST to triangle UVW is a rotation of 180°, followed by a translation 2 units left and down by 5 units.

In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;

In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.

By critically observing the geometric figures, we can reasonably infer and logically deduce that the pre-images underwent a sequence of congruence transformations to produce the images.

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