The lengths of the sides of a quadrilateral (4 sides) are consecutive even integers. Find the length of the shortest side if it is 24 units shorter than the perimeter.

Answer:

t = 1.5 hours

Step-by-step explanation:

Given that,

A man walk for 2hr at 6 km/h.

He then cycled for a certain time at 16 km/h.

He travelled 36 km all together.

We need to find for how many hours did he cycle.

Distance walked in 2 hours = 2×6 = 12 km

Distance he cycled = 36-12 = 24 km

Let he cycled for t hours. So,

\(t=\dfrac{24}{16}\\\\t=1.5\ h\)

So, he cycles for 1.5 hours.

Answer:

1½ or 1.5

Step-by-step explanation:

D = speed × time

D = 6 × 2

D = 12km ( answer to the first sentence )

2nd sentence

Speed = 16 km/h

Distance travelled all together = 36 km

Distance = x

x + 12 = 36

x = 36 - 12

x = 24km

Distance = 24km

Time = ?

T = Distance ÷ Speed

T = 24/16

T = 3/2

T = 1½ or 1.5

The value of 57.17 as a mixed number is - 57 17/100.

A mixed number is said to be in its simplest form if its fractional part's highest common factor, or HCF, is 1. When mixed numbers are simplified, the fraction value remains constant. We can say that the simplified mixed number and the actual mixed number are fractions that are equivalent.

A mixed number is made up of three components: a whole number, a numerator, and a denominator. The numerator and denominator are both components of the proper fraction that results in the mixed number.

In this case, -57.17 will be:

= -57 + (17/100)

= -57 17/100.

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Answer:

29

Step-by-step explanation:

\(2\frac{8}{10}+26\frac{2}{10} = 28\frac{10}{10} =29\)

Answer:

\(XY : WX = 1.39\)

Step-by-step explanation:

Given

\(RS = 18; ST = 25; TR = 11\)

Required

Which is closest to \(XY : WX\)

From the question, we understand that: \(\triangle RST\) and \(\triangle WXY\) are similar.

This means that, the following sides are similar:

\(RS \to WX\)

\(ST \to XY\)

\(TR \to YW\)

So:

\(XY : WX = ST : RS\)

This gives:

\(XY : WX = 25 : 18\)

Express as fraction

\(XY : WX = \frac{25 }{ 18}\)

\(XY : WX = 1.39\) --- approximated

Answer:

That would be 549.5 cubic inches of cat litter (approximately).

Step-by-step explanation: The cylindrical storage container has a height of seven inches and a radius of five inches. To know how much cat litter would fill it requires us to calculate the volume of the container.

The volume of a cylinder is given as,

Volume = Pi x r^2 x h

Where r is the radius, h is the height and Pi shall be taken as 3.14

We can now substitute for the known values as follows;

Volume = 3.14 x 5^2 x 7

Volume = 3.14 x 25 x 7

Volume = 549.5

Rounded to the nearest tenth, the container would be filled with 549.5 cubic inches of cat litter.

Answer:

The volume is 471.2 units squared.

Step-by-step explanation:

The formula for the volume of a cylinder is \(\pi r^{2} h\), where r is the radius and h is the height.

Inputting the values \(r=5\) and \(h=6\) the formula becomes \(\pi 5^{2}6\). \(5^{2}\) is 25. 25 times 6 is 150. Using a calculator to multiply by \(\pi\), we get the answer.

Answer:

corresponding

Step-by-step explanation:

<1 and <5 are corresponding angles because they are on the same side of the transversal and on the same side of l and m

Answer:

I believe the better deal would be,

Seven packs of gum for $4.00.

Answer:

  d(t) = -20t -260

Step-by-step explanation:

We are given two points ...

  (t, d) = (3, -320) and (8, -420)

The 2-point form of the equation of a line can be useful when 2 points are given.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

Substituting the given points, we have ...

  d(t) = (-420 -(-320))/(8 -3)(t -3) -320

  d(t) = -20(t -3) -320

  d(t) = -20t -260

The solution to the question is mathematically given as

1)

H0: M \(\geqslant\) 300

H0: M \(\geqslant\) 300

2)

Z distribution.

3)

z=-2.4

4)

P=0.0082

5)

"H0" is rejected as a hypothesis with a level of significance of 0.05.

Generally, the equation for is mathematically given as

Solutions

we have, \($u=300$$$\begin{aligned}& \sigma=150 \text { dollars } \\N &=64 \text { individuals } \\\bar{x} &=255 \text { dollare. } \\a=& 0.05 .\end{aligned}\)

(1):

H0: M \(\geqslant\) 300 dollars;  customers save at least 300 dollars per year by switching to them.

H0: M \(\geqslant\) 300 dollars:

(This is a left-tailed test)

(2):

when \(\sigma\) is known, we use the Z test. we use Z distribution.

(3):

\(\begin{gathered}z=\frac{\bar{x}-\mu}{6 / \sqrt{n}}=\frac{255-300}{150 / \sqrt{64}}=\frac{-45}{18.75}=-2.4 \\z=-2.4\end{gathered}\)

(4):

\(Pvalue $=P(z < -2 \cdot 4)$ $=0.0082 \quad\{$ wing $z$ tables $\}$ \\\\\text { Pvalue }=0.0082\)

(5):

In conclusion, Since p-value = 0·0082 <0.05

This is statistically significant at the 0.05 level.

We thus "Refect H0" using a threshold of significance of 0.05.

"H0" is rejected as a hypothesis with a level of significance of 0.05.

There is not enough data to support the assertion that consumers may save at least $300 annually by switching insurance providers.

Therefore, we would not consider making the transition to this firm.

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Hey ! there

Answer:

Step-by-step explanation:

In this question we are given that length of rectangle is reduced by its breadth by 8 m and Perimeter of rectangle is 128 m.

And we are asked to find the area of the rectangle.

For finding the area of rectangle firstly we need to find the length and breadth of the rectangle but their value aren't given . So we are assuming,

Solution : -

We know that ,

\( \quad \quad \underline{\boxed{\frak{Perimeter_{ ( Rectangle )} = 2 ( l + b ) }}}\)

Where ,

According to question , perimeter of rectangle is 128 m. So ,

\( \longmapsto \qquad \: 2(l + b) = 128\)

Substituting value of length and breadth :

\(\longmapsto \qquad \: 2((x - 8) + x) = 182\)

Solving parenthesis :

\(\longmapsto \qquad \: 2(x - 8 + x) = 128\)

\(\longmapsto \qquad \: 2( 2x - 8) = 128\)

Dividing with 2 on both sides :

\(\longmapsto \qquad \: \dfrac{ \cancel{2}(2x - 8)}{ \cancel{2} } = \cancel{ \dfrac{128}{2} }\)

We get ,

\(\longmapsto \qquad \:2x - 8 = 64\)

Adding 8 on both sides :

\(\longmapsto \qquad \: 2x - \cancel{ 8 }+ \cancel{8 }= 64 + 8\)

\(\longmapsto \qquad \: 2x = 72\)

Dividing with 2 on both sides :

\(\longmapsto \qquad \: \dfrac{ \cancel{2}x}{ \cancel{2} } = \cancel{ \dfrac{72}{2} }\)

\(\longmapsto \qquad \: \blue{\underline{\boxed {\frak{{x = 36 \: m}}}}} \quad \: \star\)

We know that ,

We know that ,

\( \qquad \qquad \: \underline{\boxed{\frak{Area_{ ( Rectangle )} = l \times b}}}\)

Where ,

\( \longrightarrow \quad \: 28 \times 36\)

\(\longrightarrow \quad \: \red{ \underline{\boxed{\frak{1008 \: m {}^{2} }}}} \quad \star\)

The pair of corresponding angles in the image given at the end of the answer is of:

B. 1 and 5.

Corresponding angles appear when there are two parallel lines being cut by a transversal line.

The corresponding angles are the angles that are in the same position relative to the transversal and also relative to different parallel lines.

From the image given at the end of the answer, the lines are given as follows:

Then the corresponding angles are listed as follows:

Meaning that option B is correct.

The image is given at the end of the answer.

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Answer:

your just putting the numbers at the bottom into the line plot . so let's say  there is 333 u would up the three 3 on the plot .

Step-by-step explanation:

hope this helps let me know if u need a better explanation

Answer:

y-6=2(x-5)

I hope this is good enough:

Answer: 500

Step-by-step explanation:

25 x 20 = 500

Answer:

D: 7

Step-by-step explanation:

1.75 (7) + 4.50

12.25 + 4.50

= 16.75

16.75 < 20

Answer:

puedes decirme l indicación para poder resolverlo

the final result of the double integral is `(4/3)*a. we have to Integrate the inner integral with respect to z.

what is inner integral ?

An inner integral is a mathematical term that refers to the integral function that is evaluated first in a double integral.

In the given question,

To solve this double integral, we will use the following steps:

Integrate the inner integral with respect to z.

Evaluate the result of the inner integral at  upper and lower limits of z.

Substitute the result of the inner integral into the outer integral and integrate with respect to y.

Evaluate the result of the outer integral at the upper and lower limits of y.

Simplify the expression.

Now, let's apply these steps to solve the given double integral:

Integrate the inner integral with respect to z:

∫(x²*z + y²*z + z³) dz = x²/2*z² + y²/2*z² + z^4/4 + C

where C is the constant of integration.

Evaluate the result of the inner integral at the upper and lower limits of z:

(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)

- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)

Substitute the result of the inner integral into the outer integral and integrate with respect to y:

markdown

∫[(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)

- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)] dy

Evaluate the result of the outer integral at the upper and lower limits of y:

= ∫[(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)] dy

from y = -sqrt(a²-x²) to y = sqrt(a²-x²)

= (2/3)*x²*(a²-x²)¹⁵ + (2/3)*(a²-x²)²⁵

- (2/3)*x²*(-a²+x²)¹⁵ + (2/3)*(-a²+x²)²⁵

Simplify the expression:

= (4/3)*a³ - (4/3)*a*x²

Therefore, the final result of the double integral is `(4/3)*a

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The values of the variables in number 3, in simplest radical form, are:

f = 6;  o = 3.

The simplest radical form, also known as simplified radical form or simplified surd, refers to expressing a square root (√) or other roots in the simplest possible way without any perfect square factors in the root. In other words, it involves reducing the radical expression to its simplest form.

Solving problem 3, we would apply the necessary Trigonometric ratios to find the variables:

sin 60 = opp/hyp

sin 60 = 9√3 / f

f = 9√3 / sin 60

f = 9√3 / √3/2 [sin 60 = √3/2]

f = 9√3 * 2/√3

f = 18/3

f = 6

tan 60 = opp/adj

tan 60 = 9√3 / o

o = 9√3 / tan 60

o = 9√3 / √3 [sin 60 = √3]

o = 9√3 * 1 / √3

o = 9/3

o = 3

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Answer:

o = 9

f = 18

Step-by-step explanation:

Triangle #3 is a right triangle with two of its interior angles measuring 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, this triangle is a special 30-60-90 triangle.

The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.

In triangle #3, the longest leg is 9√3 units.

As "a√3" is the shortest leg, the scale factor "a" is 9.

The side labelled "o" is the shortest leg opposite the 30° angle. Therefore:

\(o = a=9\)

The side labelled "f" is the hypotenuse of the triangle. Therefore:

\(f= 2a = 2 \cdot 9=18\)

Therefore:

Answer:

should be 1305 yd^2

Step-by-step explanation:

to get the surface area of one of the 3 recanglular sides take 24 x 15 to get 360 then muliply by 3 to get 1080 since all the recanglular sides are the same then do 15 x 15 to get both of the triangle sides to get 225 since the equation is 1/2 B x H then add them together

Answer: bellshaped

Step-by-step explanation:

The standard form of the equation of the line passing through (8,-3) that is parallel to the line 3y=4x+8 is 4x - 3y = 41

The equation of the line in standard form can be represented as follows:

Ax + By = C

where

Therefore, the standard form of the equation of the line through (8,-3) that is parallel to the line 3y = 4x + 8 is a s follows;

Parallel lines have the same slope.

Hence,

3y = 4x + 8

y = 4  / 3 x + 8 / 3

The slope of the line is 4 / 3. Hence, the line passes through (8, -3). let's find the y-intercept.

y = 4 / 3 x + b

-3 = 4 / 3 (8) + b

b = -3 - 32 / 3

b =  -9 - 32/ 3

b = -41 / 3

Hence,

y = 4 / 3 x - 41 / 3

multiply through by 3

3y = 4x - 41

Therefore, the standard form is 4x - 3y = 41

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three shapes. three areas to find. three areas to add together to find the whole area. gotcha.

Step-by-step explanation:

length is 7 cm and width is 4 cm, so the area is 28 square cm

width is 4 cm and length is 10 cm, so the area is 40 square cm

Because the weird shape's bottom length was 13 cm. There are 3 cm and 7 cm on the top length(s) of the weird shape, next to each other. Looking at the dash lines, when adding 3 cm and 7 cm together, the larger rectangle's length is 10 cm.

base is 3 cm and height is 8 cm, so the area is (3x8)/2 = 24/2 = 12 square cm

With knowledge from figuring out the larger rectangle's length being 10 cm and the weird shape's bottom length being 13 cm, we know the right triangle's base is 3 cm. (13 cm - 10 cm = 3 cm for the base of the right triangle).

Due to adding 4 cm and 4 cm of weird shape's width, which is also a right triangle's height.

28 + 40 + 12

= 80 square cm (ANSWER)

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

-3x -12

Step-by-step explanation:

-6x +3x = -3x

-3-9 = -12

Answer:

3(x+2) and 3x+6 are equivalent.

3(2x) is not.

Step-by-step explanation:

Simplify the expressions first.

1. 3(x+2) becomes 3x+6

2. 3x + 6

3. 3(2x) becomes 6x

The first and second are equivalent to each other.

The third one is not equivalent.

Hope this helped :)

Answer:

\( \frac{5}{3} \)

~ See attatchment

Step-by-step explanation:

I'm unsure what you want me to do here, so I drew a graph (using Desmos) and the slope.

The slope is given, 5/3. The slope-intercept equation is usually y = mx + b -- m being the slope and b being the y-intercept.

Hi!

Let's check if the equation that we're going to work with is in slope-intercept form.

Remember, the slope-intercept formula is:

                                   \(\diamondsuit~~~\boldsymbol{y=mx+b}\)

Where:

Details:

\(\boxed{\\\begin{minipage} {8cm}\sf{Slope = coefficient \ of \ x, \ or \ the \ number \ before \ x.}\\\sf{Y-intercept = \ a \ number \ added \ to \ or \ subtracted \ from \ the \ slope.} \end{minipage}}\)

Therefore:

\(\stackrel{\heartsuit}{\boxed{\boxed{\textsc{Slope:}\quad\boldsymbol{\displaystyle\frac{5}{3}}}}}\)

I hope I helped, have a wonderful day!

If you need any explanation or clarification, reach out to me, I'm always happy to help. :D