data visualization is important because: group of answer choices people can synthesize data better than visual representation none of these are correct everybody likes charts and graphs 90% of the information transmitted to the brain is visual

Answer:

-10

Step-by-step explanation:

the explantion is pinned in the photo

please mark me as branliest

The value of z is 20 in.

What is triangle?

A polygon that has three sides and three angles is called triangle.

In triangle QWX, we have WX || RS, so by the intercept theorem, we have:

QW/WX = QR/RS

Substituting the given values, we get:

z/(3y) = 20/(20 + y)

Cross-multiplying, we get:

20z + 3y² = 60y

We also know that:

QW + WX = QX

Substituting the given values, we get:

z + 3y = 3y

Simplifying, we get:

z = 0

Substituting this value of z into the equation we derived earlier, we get:

20z + 3y² = 60y

0 + 3y² = 60y

Dividing both sides by 3y, we get:

y = 20

Therefore, the value of z is:

z = QW = QX - WX = 3y - 2y = y = 20

So, z = 20

Therefore required value of z is 20 in.

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1. Identify the curve and the point: The curve is y = sec(x), and the point is (π/6, 2√3/3).

2. Calculate the derivative of the curve: The derivative of y = sec(x) is y' = sec(x)tan(x).

3. Evaluate the derivative at the given point: At x = π/6, we have y' = sec(π/6)tan(π/6). Since sec(π/6) = 2 and tan(π/6) = √3/3, we get y' = 2(√3/3) = 2√3/3.(4). Use the point-slope form of the line equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope (derivative).

5. Plug in the values: y - (2√3/3) = (2√3/3)(x - π/6). This is the equation of the tangent line to the curve y = sec(x) at the point (π/6, 2√3/3).

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The probability of winning the minimum prize is approximately 0.00014

To calculate the probability of winning this minimum prize, we need to first find out the total number of possible combinations of numbers that can be drawn.

There are 56 white balls, and 5 balls are drawn from them, so the total number of possible combinations of white balls is

56 choose 5 = 56! / (5! (56-5)!) = 3,819,816

There are 46 gold balls, and only 1 is drawn from them. Therefore, the total number of possible combinations of gold balls is simply 46.

To win the minimum prize, we need to correctly match 4 out of the 5 white balls drawn, and we also need to match the gold ball.

The number of ways to choose 4 white balls out of 5 is

5 choose 4 = 5! / (4! (5-4)!) = 5

So, the total number of ways to win the minimum prize is the product of the number of ways to choose 4 white balls and the number of ways to choose 1 gold ball

Total number of ways to win the minimum prize = 5 × 46 = 230

Therefore, the probability of winning the minimum prize is

Probability = number of ways to win the minimum prize / total number of possible combinations

Probability = 230 / (3,819,816 × 46) = 0.00014

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The area of the parallelogram  will be equal to 60 in²

Since it's a parallelogram so,  area of a parallelogram is the product of the base and the height of the figure.

area of a parallelogram = Base x Height

We are given that area of a parallelogram = Base x Height

A = bh

A =  6×1 0

A = 60 in²

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Leroy's total employment compensation last year was $46,650. Hence, the correct answer is option a, $46,650.

To find Leroy's total employment compensation, we need to consider his total job benefits and his total job expenses for traveling and professional development.

Leroy's total job benefits last year were $50,150. His total job expenses for traveling and professional development were $3,500. To calculate his total employment compensation, we need to subtract the job expenses from the job benefits.

Total employment compensation = Total job benefits - Total job expenses
Total employment compensation = $50,150 - $3,500
Total employment compensation = $46,650

The correct option is a. $46650.

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Answer:Width=5, Length=10

Step-by-step explanation:

You can solve this by using a variable, x, and assigning it to the value that is the width.

Since the perimeter of a rectangle is the width times two plus the length times two, you can use an equation that looks like this:

(image shown)

This will give you the value of X, the width, and you can multiply this value by 2 to get the length.

Answer:

10 cm

Step-by-step explanation:

The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length and w is the width1. We know that the perimeter of this rectangle is 30 cm. So we can write:

2(2w + w) = 30

Simplifying this equation gives:

6w = 30

Therefore:

w = 5

So the width of the rectangle is 5 cm and its length is twice as long as its width which means it’s 10 cm.

With a significance level of 0.05 for a one-tailed test, the critical value is 1.761. Since -1.86 is less than -1.761, we reject the null hypothesis.

To test for significant increases in average domestic business charges over a one-year period, you can use a paired-sample t-test.

This is good because the two sets of observations (current year and previous year) are paired on the same flight.

The null hypothesis (H0) states that the average domestic fares for business travel are not significantly different from the previous year.

The alternative hypothesis (Ha) indicates that average domestic fares for business travel will increase significantly this year compared to the previous year.

This can be written as:

H0:

µd = 0

teeth:

µd > 0

where μd is the population mean of the differences in domestic fares between the current year and the previous year.

To do the test, to begin with, calculate the contrast between the residential passages for the current year and the past year.

At that point calculate the mean and standard deviation of these contrasts.

 d = (558-219) + (417-312) + ... + (348-369) / 15

= -15.2

s = sqrt([(558-219+15.2)^2 + ... + (348-369+15.2)^2] / (15-1))

= 134.8

The t-statistic for the test is

t = (d - 0) / (s / sqrt(n))

= (-15.2 - 0) / (134.8 / square(15))

= -1.86

Using a one-sided test with 14 (n-1) degrees of freedom and a t table with a significance level of 0.05, the critical value is 1.761. -1.86 is less than -1.761, so we reject the null hypothesis.

It can in this manner be concluded that there's adequate proof to back the claim that the normal household airfare for trade travel has expanded essentially over the years. 

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Answer:

Height 15 feet

Base 12 Feet

Step-by-step explanation:

The formula to find the area of a triangle is A= (0.5) x base x height, so if the area is 90 then before it was halved it must be 180 so the base x height must equal 180 and the only number that equal 180 when multiplied with a difference of 3 between them is (15,12) so thats are answer. I know this is right because if I put it through the area formula I get 90.

A=(.5) x 12 x 15

A=(.5) x 180

A= 90

The vertex of the absolute value function is (-3, 2).

The range of the function is 2 < y < ∞.

Option C is the correct answer.

We have,

To find the vertex of the given absolute value function, we can first find the vertex of the related linear function, which is y = 2x + 6.

The vertex of this linear function is (-3, 0), obtained by setting x = -3 to find the minimum value of the linear function.

Since the given absolute value function has the same shape as the related linear function but is shifted up by 2 units,

The vertex of the absolute value function is (-3, 2).

To find the range of the function, note that the absolute value of 2x + 6 is always non-negative.

Thus, the smallest possible value of the function is 2 (when 2x + 6 = 0) and the function is unbounded above.

Therefore, the range of the function is 2 < y < ∞.

Therefore,

The vertex of the absolute value function is (-3, 2).

The range of the function is 2 < y < ∞.

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The expression that is equivalent to 43,450,000 when simplified is 4.345 x 10⁷

43,450,000 is the numerical expression given, and it can be simplified by breaking it down into its factors of 10.

In scientific notation, a number can be expressed in the form of a x 10^b, where a is a number between 1 and 10 and b is an integer that represents the number of places the decimal point has been moved.

To simplify 43,450,000, we can write it as

4.345 x 10⁷

This is because we have moved the decimal point seven places to the left.

So, the expression that is equivalent to 43,450,000 when simplified is

4.345 x 10⁷

This notation is commonly used in science and engineering to represent very large or very small numbers, as it makes it easier to work with such values.

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Answer:

Given information:

To obtain the equation of the regression line for the given data.

The equation of regression line of y on x is given by:

y

−

¯

y

=

b

y

x

(

x

−

¯

x

)

;

w

h

e

r

e

,

y

=

d

e

p

e

n

d

e

n

t

v

a

r

i

a

b

l

e

x

=

i

n

d

e

p

e

n

d

e

n

t

v

a

r

i

a

b

l

e

b

y

x

=

s

l

o

p

e

o

f

r

e

g

r

e

s

s

i

o

n

l

i

n

e

¯

x

=

m

e

a

n

o

f

x

¯

y

=

m

e

a

n

o

f

y

y−y¯=byx(x−x¯);where,y=dependentvariablex=independentvariablebyx=slopeofregressionlinex¯=meanofxy¯=meanofy

The calculations for the equation of regression line is tabulated below:

The regression coefficient of y on x is given by:

b

y

x

=

∑

x

y

−

1

n

∑

x

∑

y

∑

x

2

−

1

n

(

∑

x

)

2

=

1944

−

1

5

×

98

×

69

2580

−

1

5

(

98

)

2

=

591.6

659.2

=

0.898

byx=∑xy−1n∑x∑y∑x2−1n(∑x)2=1944−15×98×692580−15(98)2=591.6659.2=0.898

Mean of x is calculated as:

¯

x

=

1

n

∑

x

=

1

5

×

98

=

19.6

x¯=1n∑x=15×98=19.6

Mean of y is calculated as:

¯

y

=

1

n

∑

y

=

1

5

×

69

=

13.8

y¯=1n∑y=15×69=13.8

The equation of regression line is given as:

y

−

¯

y

=

b

y

x

(

x

−

¯

x

)

y

−

13.8

=

0.898

(

x

−

19.6

)

y

=

0.898

x

−

3.8

y−y¯=byx(x−x¯)y−13.8=0.898(x−19.6)y=0.898x−3.8

Therefore, the required equation of regression line is y = 0.898x - 3.8.

Answer: BC = 8.94

Step-by-step explanation:

      Since this is a right triangle, we can use the Pythagorean theorem. a and b are the triangle legs and c is the hypotenuse.

a² + b² = c²

19² + b² = 21²

361 + b² = 441

b² = 80

b = [tex]\sqrt{80}[/tex]

b ≈ 8.94

BC = 8.94

The length of line AC of the given quadrilateral ABCD would be = 13.7cm

To calculate the length of line AC is to calculate the length of CE and AE separately and add up the lengths afterwards.

The length of CE can be calculated using Pythagorean formula;

That is C² = a² +b²

where C = 8cm

a = 5cm

b = CE = ?

b² = 8²-5²

b = 64-25

b² = 39

b =√39

b = 6.2

For AE;

b² = AE = 9²-5²

= 81-25

= 56

b = √56

= 7.5

Therefore the length of AC = 6.2+7.5 = 13.7cm

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The proof is completed using the properties of equality

The two column proof is completed as below

Statement                                              Reason

angle 2 ≅ angle 4                                  Given

angle 1 + angle 2 = 90 deg                   definition of right triangle

angle 3 + angle 4 = 90 deg                  definition of right triangle

angle 1 + angle 2 = angle 3 + angle 4  substitution property of equality

angle 1 + angle 4 = angle 3 + angle 4  substitution property of equality

angle 1 = angle 3                                   addition property of equality

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Answer:

a)1/12

b)3/4

c)5/12

d)2/3

Step-by-step explanation:

let chocolate bar be C

let fruit chew be F

let Pack of buble gum be =B

1let sour Candie be S

C=4

F=4

B=1 pack

S=3

T=4+4+1+3=12

a) 1/12

b)9/12=3/4

c)4/12+1/12=1/3+1/12=5/12

d)8/12=2/3

Answer:

7/14 in simplest form is 1/2

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Orthogonal matrix A that satisfies the given conditions is:

[3 3 0 ]

[1/√(2) -1/√(2) √(2/9)]

[-√(2)/2 √(2)/2 √(2)/2]

Let's call the first row of matrix A as r1, which is a multiple of (3, 3, 0). Since the length of a row vector of an orthogonal matrix is always 1, we can find a unit vector that is orthogonal to (3, 3, 0).

One such vector is (3, -3, 2), which can be verified by checking that the dot product of (3, 3, 0) and (3, -3, 2) is zero.

To obtain the second row of A, we can normalize the vector (3, -3, 2) to have a length of 1. This gives us:

(3, -3, 2)/√(18) = (1/√(2), -1/√(2), √(2/9))

To obtain the third row of A, we can take the cross product of the first two rows to get a vector that is orthogonal to both. This gives us:

(3, 3, 0) x (1/√(2), -1/√(2), √(2/9)) = (-2√(2)/3, 2√(2)/3, 2√(2)/3)

We can then normalize this vector to obtain the third row of A:

(-2√(2)/3, 2√(2)/3, 2√(2)/3)/√(8/9) = (-√(2)/2, √(2)/2, √(2)/2)

Therefore, the orthogonal matrix A that satisfies the given conditions is:

[3 3 0 ]

[1/√(2) -1/√(2) √(2/9)]

[-√(2)/2 √(2)/2 √(2)/2]

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The angle in standard position is  150°

The angle of any position (x, y) on a graph is given by Ф = tan⁻¹(y/x).

Now given the position (-√3, 1) on the graph, to find the angle in standard position, we proceed as follows.

To find the angle, we substitute the values of the variables into the equation. so, we have that

Ф = tan⁻¹(y/x)

Given that

Ф = tan⁻¹(y/x)

Ф = tan⁻¹(1/-√3)

= tan⁻¹(-1/√3)

= 180° - tan⁻¹(1/√3)

= 180° - 30°

= 150°

So, the angle is  150°

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The number of  hours it would take 6 pipes to fill 1/4 of the lake is 4.5 hours

Given that

It takes 4 of the pipes 12 hours to fill the lake.

This means that

Rate = 12 hours/4 pipes

So, we have

Rate = 3 hours/ pipe

For 6 pipes to fill 1/4 of the lake. we have

Time = 3 hours *6 * 1/4

Evalaute

Time = 4.5 hours

Hence, the time taken is 4.5 hours

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The total amount of money that Mavis with 33 nickels, 67 dimes, 19 quarters, and 14 fifty-cent pieces has is C. $20.10.

The total amount that Mavis has can be determined by the multiplication of the cents based on their unit values.

Multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.

33 nickels = $1.65 (33 x $0.05)

67 dimes = $6.70 (67 x $0.10)

19 quarters = $4.75 (19 x $0.25)

14 fifty-cents = $7.00 (14 x $0.50)

Total amount = $20.10

Thus, Mavis has a total amount of $20.10.

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If the width of the rectangle is 21 inches, the length is 24.5cm and the area is 372cm²

A  rectangle is described as a quadrilateral with four right angles.

suppose we have the width of rectangle = 21 inches

therefore:

( x + 0.5) = 21

x = 20.5

Area of rectangle =  we multiply the length of the rectangle by the width of the rectangle.

 2x² + 9x + 4

Area of rectangle = 2(11.5)² + 9(11.5) + 4

=  372cm²

length of rectangle = x + 4

length of rectangle= 20.5 + 4

length of rectangle = 24.5cm

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We can use the distributive property and the greatest common factor to write 36 + 4 as 4(9 + 1) or 4(10).

Using the distributive property, we can write:

36 + 4 = 4(9 + 1)

Next, we can identify the greatest common factor (GCF) of 9 and 1, which is 1. Since there are no other common factors between 9 and 1, we can write:

9 + 1 = 10

Therefore, we can express 36 + 4 as:

36 + 4 = 4(9 + 1) = 4(1 × 9 + 1) = 4(10)

So, 36 + 4 can be written as the product of 4 and 10, where 4 is the GCF of 36 and 4, and 10 is the sum of the two terms divided by their GCF. This is an example of factoring by grouping, which can be a useful technique in algebra and other areas of mathematics.

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Mark sets aside $404 for more supplies.

Mark spent $175 on supplies, so his total cost is $175.

Mark sold 6 pieces of artwork for $70 each, so he earned 6 * $70 = $420 from these pieces.

He sold 15 - 6 = 9 pieces of artwork at $85 each, so he earned 9 * $85 = $765 from these pieces.

His total revenue is $420 + $765 = $1185.

His profit is his revenue minus his cost: $1185 - $175 = $1010.

He plans to set aside 40% of his profit for more supplies, so he will set aside 0.4 * $1010 = $404.

Therefore, Mark sets aside $404 for more supplies.

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Answer:

The parrot is 48 years old and knows 76 words.

Step-by-step explanation:

The outlier is far away from all the other points on the y-axis and the x-axis.

The graphs to match each inequality to its solution are added as an attachment

Analyzing the inequalities from the question, we have the following explanations

Next, we match the number lines and the inequalities

See attachment for number lines

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Step-by-step explanation:

there are 2 formulas to calculate the length of a chord, depending on what pieces of information we have.

here now we have the length of the chord, which we need to find the radius, which we need to find the angle at the center.

chord length = 2×sqrt(r² - d²)

chord length = 2×r×sin(c/2)

r is the radius, d is the distance of the chord from the center of the circle, c is the angle of the chord at the center of the circle.

20 =2×sqrt(r² - 12²) = 2×sqrt(r² - 144)

10 = sqrt(r² - 144)

100 = r² - 144

244 = r²

r = 15.62049935... cm

20 = 2×r×sin(c/2) = 2×15.62049935...×sin(c/2)

10 = 15.62049935...×sin(c/2)

sin(c/2) = 10/15.62049935... = 0.6401844...

c/2 = 39.80557109...°

c = 79.61114218...° ≈ 79.6°

(a) the angle subtended by the chord at the center of the circle is about 79.6°.

(b)

the arc length of a segment is 2pi×r × c/360

in our case

2×3.142×15.62049935...×79.61114218.../360 =

= 21.70713182... cm

the whole perimeter of the segment is then arc length + chord length =

= 21.70713182... + 20 = 41.70713182... ≈ 41.7 cm

the perimeter of the minor segment cut off by the chord is about 41.7 cm.

Answer:

13*

Step-by-step explanation:

Use the Pythagorean theorem.

a=1

b=x

c=13

so, [tex]1^2 + x^2 = 13^2[/tex]

[tex]x^2 = 169 - 1 = 168[/tex]

[tex]x = \sqrt{168}[/tex]

 [tex]\sqrt{168} = 12.961481396815720461931934872176[/tex] = 13

*If we round to the nearest tenth, we get 13. Because of this rounding, the other leg is the hypotenuse, but it is actually different.