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bogdanovich [222]
3 years ago
12

A winter resort took a poll of its 400 visitors to see which winter activities people enjoyed. The results were as follows: 188

liked to ski, 144 liked to snowbiard, 67 liked to ice skate, 39 liked to ski and snowboard, 35 liked to ski and ice skate, 10 liked to snowboard and ice skate, 5 liked all three activities. Use a Venn diagram to determine how many of those surveyed enjoyed exactly one of these activities. none of these activities. at least two of these activities . snowboarding and ice skating, but not skiing, snowboarding or ice skating, but not skiing. only skiing
Mathematics
1 answer:
VARVARA [1.3K]3 years ago
6 0
Exactly one activity:  246
None of the activities :  1
At least one activity:  74
Snowboarding and Ice skating but not skiing:  5
Snowboarding or ice skating but not skiing:  132.
Only skiing :  119.
The diagram is in the attachment. 
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The sum of squares of two consecutive odd numbers is 514 find the numbers ​
amid [387]

Correct Question : The sum of squares of two consecutive positive odd numbers is 514. Find the numbers.

\rule{130}1

Solution :

Let the two consecutive positive odd numbers be x and (x + 2)

\rule{130}1

☯ \underline{\boldsymbol{According\: to \:the\: Question\:now :}}

:\implies\sf x^2 + (x + 2)^{2} = 514 \\\\\\:\implies\sf x^2 + x^2 + 4x + 4 = 514\\\\\\:\implies\sf 2x^2 + 4x + 4 = 514 \\\\\\:\implies\sf 2x^2 + 4x = 514 - 4\\\\\\:\implies\sf 2x^2 + 4x = 510 \\\\\\:\implies\sf 2x^2 + 4x - 510 = 0\\\\\\:\implies\sf x^2 + 2x - 255 = 0 \:\:\:\:\:\Bigg\lgroup \bf{Dividing\:by\:2}\Bigg\rgroup\\\\\\:\implies\sf x^2 + 17x - 15x - 255 = 0\\\\\\:\implies\sf x(x + 17) - 15(x + 17) = 0\\\\\\:\implies\sf (x + 17) (x - 15)\\\\\\:\implies\sf x = - 17\:or\:x = 15\\\\\\:\implies\underline{\boxed {\sf x = 15}}\:\:\:\:\:\Bigg\lgroup \bf{Positive\:odd\: number}\Bigg\rgroup

When,

\bullet\: \textsf {x = } \textbf {15}

\bullet\: \sf x + 2 = 15 + 2 =\textbf{ 17}

\therefore\:\underline{\textsf{The required positive integer is \textbf{15 and 17}}}.

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3 years ago
Write the equation of a line perpendicular to y=-5x that passes through the point (1,1) in slope intercept form. (This question
Kazeer [188]

Answer:

y= 1/5x + 0.8

Step-by-step explanation:

Hope this helps

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3 years ago
A rectangular prism has a volume of 19 cm if the length of the prism is tripled and the other dimensions stay the same what is t
eimsori [14]

Answer:

The volume of the new prism is three times the volume of the old prism

Step-by-step explanation:

To carry out this problem we have to invent 3 variables that represent length, width and height

w = width

h = height

l = length = 19cm

Now we have to do the equation that represents the calculation of the volume of the prism

v = w * h * l

v = w * h * 19

v = 19hw

assuming the length is tripled

v = w * h * 3l

v = w * h * 3 * 19

v = 57wh

To know the volume of the new prism with respect to the previous one, we simply divide the volume of the new prism by the previous one.

57hw / 19hw = 3

The volume of the new prism is three times the volume of the old prism

6 0
3 years ago
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Please help me answer this!
Tomtit [17]

Answer:

<em>x = 3</em>

Step-by-step explanation:

<u>Trigonometric Ratios</u>

The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of a right triangle is called the hypotenuse and the other two sides are the legs.

The tangent ratio relates the opposite leg with the adjacent leg. Please note the given side is the opposite leg to 60° and x is the adjacent leg to 60°, thus we apply the tangent ratio:

\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}

\displaystyle \tan 60^\circ=\frac{3\sqrt{3}}{x}

Solving for x:

\displaystyle x=\frac{3\sqrt{3}}{\tan 60^\circ}

Since:

\tan 60^\circ=\sqrt{3}:

\displaystyle x=\frac{3\sqrt{3}}{\sqrt{3}}

Simplifying:

x = 3

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Answer:

yellow I believe is the answer

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3 years ago
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