A triangle has sides with lengths of 65 kilometers, 72 kilometers, and 97 kilometers. Is it a
right triangle?

Answer:

-7y > 161

7y < -161

y < -23

7y > -161

y > -23

So, your answer is: -7y > 161 is equal to y < -23, and 7y > -161 is equal to y>-23.

Let me know if this helps!

Answer:

Yes, because 9 is in the hundreths place and 3 is in the tenths

Step-by-step explanation:

Answer:

Step-by-step explanation:

no because 0.3 is the same as 3/10 and 0.9 is the same as 9/10 wich is greater

The amount of candy each person gets is given by the equation A = 1/20 of the candy

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount of candy each person receives is A

Now , the amount of candy = 1/5 of the candy

The number of friends = 4 friends

So , the amount of candy each person gets A = amount of candy / number of friends

Substituting the values in the equation , we get

The amount of candy each person gets A = ( 1/5 ) / 4

On simplifying the equation , we get

The amount of candy each person gets A = 1/20 of the candy

Hence , the equation is A = 1/20

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Answer:

40+s

Step-by-step explanation:

Answer:

40+s

Step-by-step explanation:

Matt has 40 big spoons.

He has s small spoons.

We need to add these together to find the total number of spoons.

It would simply be number of big spoons plus number of small spoons.

Therefore, the expression would be 40+s

The probability is 0.3845.The probability of anything occurring is known as probability.

Explanation:

2/52 * 10/52  = 20/52 = 0.3845.

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Answer:

-6

Step-by-step explanation:

-8=-2x+4    -8-4=2x   -12=2x  x= -12:2   x= -6

Answer:

$42.75

Step-by-step explanation:

Answer:

94.8

Step-by-step explanation:

sin 45 = 67/x

x = 67/sin 45

x = 94.8

Hello there. To solve this question, we have to determine the solutions to the quadratic equation shown in the graph.

For this, we simply have to find, by inspection, the points for which it is equal to zero, that is, when it crosses the x-axis:

It is easy to see that is passes through the points x = -3 and x = 2, since the coordinate plane was divided into a lot of squares with side length equal to 1.

Hence we say that the answer to this question is:

This is the answer and it is contained in the third oval.

It took longer than a half-hour time but less than an hour because 5/12<1/2, so 5/12 + 1/2 < 1. So correct option is D.

Mathematical relationships and operations that are represented by symbols and letters are the subject of the discipline of mathematics known as algebra. It entails representing unknowable quantities with letters, symbols, and numbers while also manipulating these symbols to solve mathematical puzzles.

In algebra, we explain relationships between variables using equations and inequalities. Letters are commonly used to denote variables, and equations show how the variables relate to one another. Addition, subtraction, multiplication, and division are the four fundamental algebraic operations that humans utilise to manipulate equations and find solutions to issues.

Numerous disciplines, including science, engineering, economics, and finance, use algebra. It is an effective technique for tackling challenging issues and is necessary in many advanced areas of mathematics.

The amount of time Nolan spent reading and tending to his garden is equal to the sum of his reading time (5/12 hour) and his gardening time (1/2 hour). As a result, we must determine the product 5/12 plus 1/2:

5/12 + 1/2 = (5/12) x (2/2) + (1/2) x (6/6) = 10/24 + 12/24 = 22/24

When we simplify the ratio 22/24, we obtain:

22/24 = 11/12

As a result, Nolan spent 11/12 hours reading and tending to his garden, which is more than 1/2 hour but less than 1 hour.

So, D is the right response. It took longer than a half-hour but less than an hour because 5/12<1/2, so 5/12 + 1/2 < 1.

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The complete question is,

a) Nonzero vector orthogonal to the plane through the point P(0, 0, -3), Q(4,2, 0), and R(3, 3, 1) would be (12, -6, -12)

b) Area of the triangle PQR would be 4.18

What is nonzero vector of orthogonal ?

Taking the cross product of two vectors in the plane yields a non-zero vector orthogonal to the plane across the points. Calculate the difference vector of two of the points, then take the cross product of that difference vector with the difference vector of the third point.

a) A nonzero vector orthogonal to the plane through the points P, Q, and R can be found by taking the cross product of two nonparallel vectors in the plane.

For example, the vector PQ = (4, 2, 0) - (0, 0, -3) = (4, 2, 3) and PR = (3, 3, 1) - (0, 0, -3) = (3, 3, 4). The cross product of these vectors is orthogonal to the plane:

PQ x PR = (12, -6, -12)

2) The area of triangle PQR can be found using the cross product formula for the area of a parallelogram. The area is given by the magnitude of the cross product of two sides of the triangle:

         \(Area =\frac{ |PQ * PR| }{2}\\\\Area =\frac{\sqrt{(12^2 + (-6)^2 + (-12)^2)} }{2}\\\\Area =3 * \sqrt(10) / 2\\\\Area =4.18\)

Thus, Nonzero vector orthogonal to the plane through the point P(0, 0, -3), Q(4,2, 0), and R(3, 3, 1) would be (12, -6, -12) and area of the triangle PQR would be 4.18.

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To determine the variance of a geometric random variable X with parameter p, we can use the conditional variance formula.

The formula for the variance of a geometric random variable is given by:

Var(X) = (1 - p) / (p^2)

Where p is the parameter of the geometric distribution, representing the probability of success on each trial.

This formula assumes that the random variable X represents the number of trials required until the first success in a sequence of independent Bernoulli trials, where each trial has a probability of success p.

By plugging in the value of p into the formula, you can calculate the variance of the geometric random variable X.

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The probability that a woman was wearing a belt given that she was also carrying a purse is 0.333 or 33.3%.

To find the probability that a woman was wearing a belt given that she was also carrying a purse, we need to use conditional probability.

We know that out of the 30 women observed, 18 were carrying purses and 6 were both carrying purses and wearing belts.

This means that the number of women carrying purses who were also wearing belts is 6.
Therefore, the probability that a woman was wearing a belt given that she was also carrying a purse is:
P(wearing a belt | carrying a purse) = number of women wearing a belt and carrying a purse / number of women carrying a purse
P(wearing a belt | carrying a purse) = 6 / 18
P(wearing a belt | carrying a purse) = 0.333
Given the information provided, we can determine the probability of a woman wearing a belt, given that she is also carrying a purse.

First, we need to find the number of women carrying a purse and wearing a belt, which is 6. There are 18 women carrying purses in total.
So, to find the probability, we will use the formula:
P(Belt | Purse) = (Number of women wearing belts and carrying purses) / (Number of women carrying purses)
P(Belt | Purse) = 6 / 18
P(Belt | Purse) = 1/3 or approximately 0.33
Therefore, the probability that a woman was wearing a belt, given that she was also carrying a purse, is 1/3 or approximately 0.33.

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Answer: A

Step-by-step explanation:

X=1

The correct statement among the given options is A. "Research cannot use both qualitative and quantitative methods in a study."

This statement is not correct because research can indeed use both qualitative and quantitative methods in a study. Qualitative research focuses on collecting and analyzing non-numerical data such as observations, interviews, and textual analysis to understand phenomena in depth. On the other hand, quantitative research involves collecting and analyzing numerical data to derive statistical conclusions and make generalizations.

Many research studies employ a mixed methods approach, which combines both qualitative and quantitative methods, to provide a comprehensive understanding of the research topic. By using both qualitative and quantitative data, researchers can gather rich insights and statistical evidence, allowing for a more comprehensive analysis and interpretation of their findings.

Therefore, option A is the statement that is not correct concerning qualitative and quantitative research.

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Answer:

See below

Step-by-step explanation:

1. The sum of two numbers is 72. Lets say the two numbers are x and y:

   x + y = 72

If one number is 3 times the other,

  x = 3y

what is the largest number?

 Substitute the second into the first expression

x + y = 72

3y + y = 72

4y = 72

 y = 18

2.  From 6:30am to noon is 5 1/2 hours.  From noon to 1:30 is another 1 1/2 hours.  The sum is (5.5 + 1.5) = 7 hours

3.  I'm assuming the bottom two angles are the same (diffiuclt to read).  If so, we know that the sum of the interior angles of a triangle is 180 degrees.  

        2x + x + x = 180

        4x = 180

          x = 45 degrees

4.  (1.5 meters)*($22.50/meter) = $33.75

5.  (0.5 L)*(1000 ml/L) = 500 ml

The correct option is D. the number of sweatshirts for which cost and income are equal.

Any equation that contains only one element which squares the variable and none that raises it to a higher power.

The general form form of quadratic equation is-

ax² + bx + c = 0

According to the question;

Use the substitute method to get the quantity of sweatshirts in which cost and earnings are equal.

Step 1: Write the following system of equations as the first step.

\(\begin{aligned}&y=35 x \\&y=-0.05(x-400)^{2}+9492\end{aligned}\)

Step 2: Replace the value of "y" in the equation (2).

\(35 x=-0.05(x-400)^{2}+9492\)

Step 3: Make the equation above simpler.

\(35 x=-0.05 x^{2}-8000+40 x+9492\)

Step 4: Write the preceding equation in generalised quadratic form.

\(0.05 x^{2}-5 x-1492=0\)

The processes above lead to the conclusion that option D provides the proper statement.

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The complete question is-

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league. What does the solution of the system represent in this context?

y=35x

y=-0.05(x-400)^2+9,492

A. the number of sweatshirts that generate the maximum income

B. the number of sweatshirts that generate the minimum cost

C. the number of sweatshirts for which the difference between cost and income is greatest.

D. the number of sweatshirts for which cost and income are equal

Answer:

D

Step-by-step explanation:

He said so

Answer:

C. AB = 10.7

Step-by-step explanation:

Let's look through each option.

Option A

❌ AB = 2(AC)

It can't be that since AC isn't equivalent to BC. AC is 5.5 and CB is 5.2

Option B

❌ AB = 11

AB doesn't equal 11. AB equals to AB + AC.

If you put the numbers in, it gets to AB = 5.5 + 5.2.

If you add the numbers up, it would get to AB = 10.7. Since 10.7 is not 11, option B won't work.

Option C

Option C works as shown in Option B.

Option D

none of the above isn't true since option C works.

Hope this helped! If not, please let me know! <3

The value of radius of a right circular cylinder is 1,248 in for which the minimum surface area is obtained.

Volume of the  right circular cylinder be;

v(c) = 12 in³ =  π*r²*h    

In which, h is the height of the cylinder,

Then , h  =  12 / π*r²

Surface area of a right circular cylinder is:

S = area of base and top  + lateral area

S(A)  =  2*π*r²  + 2*π*r*h  ....eq 1

Put value of 'h' in equation (1)

S(r)  =  2*π*r² +   2*π*r*  ( 12 / π*r²)

S(r)  =  2*π*r² + 24 /r

Differentiate both sides,

S´(r)  =  4*π*r -  24 /r²

Put , S´(r)  = 0 to get the critical points.

4*π*r -  24 /r²  =  0

π*r - 6/r² = 0

π*r³ - 6  = 0

r³   =  1,91    

r = 1,248 in    

Check for the minimum surface area for r = 1,248 in.

Find the second derivative,

S´´(r)  =  4*π  +  48/r³    

S´´(r)  will always be positive.

Thus,  the minimum surface area S  is for   r = 1,248 in.

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Answer:

3 pi.

Step-by-step explanation:

Answer:

5km

Step-by-step explanation:

15 km/ hr x 1 hr/ 60 min = 15/60 km/min = 5/20 km/min

5/20 km/min x 20 min=5 km

The tangential component of the acceleration vector represents the change in speed or direction along the path. The normal component of the acceleration vector represents the change in direction perpendicular to the path.

To find the tangential and normal components of the acceleration vector, we need the velocity vector and the curvature of the path. The tangential component of acceleration (at) represents the change in speed or direction along the path. It is given by the derivative of the velocity vector with respect to time. The normal component of acceleration (an) represents the change in direction perpendicular to the path. It is given by the curvature of the path multiplied by the square of the speed.

In mathematical terms:

at = dV/dt

an = (V^2) / R

where:

V is the velocity vector

t is time

R is the radius of curvature of the path.

The tangential component of the acceleration vector represents the change in speed or direction along the path. The normal component of the acceleration vector represents the change in direction perpendicular to the path.

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M = slope (ride over run) ( pick any two coordinates on the slope line)

B = y-intercept (where the y-axis crosses over the x-axis

So now plug it in.

M = 1 bc 3/3=1

B = 6

Y = 1x+6

Answer:

  138, 139

Step-by-step explanation:

You want the consecutive page numbers whose total is 277.

Consecutive integers differ by 1. If the lesser of two consecutive integers is represented by x, then the next one is (x+1). The sum of these two integers will be ...

  x + (x +1) = 2x +1

We want to find the numbers whose sum is 277:

  2x +1 = 277

  2x = 276

  x = 138

  x+1 = 139

The two page numbers are 138, 139.

__

Additional comment

It is customary for the odd page number to be on the right when the book is open. Fortunately, this problem makes that be the case.

Therefore, two page numbers are 138, 139 of a left and right page numbers of an open book are two consecutive integers whose sum is 277.

Positive numbers, negative numbers, and zero are examples of integers. 'Integer' is a Latin word that means 'complete' or 'completely'. This means that integers exclude fractions and decimals. In this article, we'll learn more about integers, their definition, and their properties.

All whole numbers & negative numbers are considered integers. This means that if we combine negative and whole numbers, we get a set of integers.

The difference between two consecutive integers is 1. The following integer is (x+1) if x is the lesser of two subsequent integers. These two integers' sum will be

x + (x +1) = 2x +1

So for 277 the equation will be

⇒  2x +1 = 277

⇒  2x = 276

⇒  x = 138

⇒  x+1 = 139

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The volume of the resulting frustum is approximately 1533.33 cubic centimeters.

Here's a sketch of the resulting frustum:

       ____

  ___/    \___

__/            \__

/

/

/ \

In this diagram, the original cone is represented by the larger shape, and the resulting frustum is represented by the smaller shape on top. The horizontal cut that Andy made is shown as the straight line near the top of the larger shape.

To find the volume of the resulting frustum, we can use the formula:

V = (1/3)πh(R^2 + r^2 + Rr)

where h is the height of the frustum (which is 20 - 8 = 12 cm), R is the radius of the base of the original cone (which is 5 cm), and r is the radius of the top of the frustum (which we need to calculate).

To find r, we can use similar triangles. If we draw a line from the center of the base of the cone to the point where the cut was made, we create two similar triangles: one with height 8 cm and base radius r, and another with height 20 - 8 = 12 cm and base radius 5 cm. Using the ratios of corresponding side lengths, we get:

r/8 = 5/12

Multiplying both sides by 8 gives:

r = (5/12)*8 = 20/3 cm

Now we can plug in all the values into the formula for the volume:

V = (1/3)π12(5^2 + (20/3)^2 + 5*(20/3))

= (1/3)π12(25 + 400/9 + 100/3)

= (1/3)π12(1150/9)

= 1533.33... cubic centimeters (rounded to two decimal places)

Therefore, the volume of the resulting frustum is approximately 1533.33 cubic centimeters.

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A box and whisker plot is the appropriate display for the data, as it shows the minimum and the maximum value of the data-set, while the range is the difference of the maximum value by the minimum value.

From left to right, the five features of the box and whisker plot are listed as follows

The range of a data-set is given as follows:

Range = Maximum value - Minimum value.

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Answer:

2

Step-by-step explanation:

Just use the quadratic formula

Answer:

$17.25

Step-by-step explanation:

The tip is 15% of $15.00, or 0.15 * 15 = $2.25

We add that to the meal's cost, which is $15.00

15.00 + 2.25 = 17.25

Answer:

196 miles

Step-by-step explanation:

distance (D) is calculated as

D = S × T ( S is average speed and T is time in hours )

here T = 3 and a half hours = 3.5 hours and S = 56 , then

D = 56 × 3.5 = 196 miles